NEW DELHI—One morning in late May, hundreds of people from an upscale housing complex in a Mumbai suburb lined up to receive their first dose of a Covid-19 vaccine. Unbeknown to them, they got a shot of saline solution.

Authorities say the scam was one of the largest of several that have led to thousands of people receiving fake vaccines in India. The global vaccine rollout has presented an opportunity for criminals, particularly in the developing world where doses have been in short supply.

In April, Pfizer Inc. said it had identified counterfeit versions of a vaccine it developed with BioNTech SE in Mexico and Poland. In South Africa last year, authorities found 2,400 doses of illicit vaccines in a warehouse. Interpol said in March that it had identified a network connected to the bust and raided a lab in China where they were allegedly being produced.

Police in India have recently made arrests in Mumbai, New Delhi and Kolkata, charging people with trying in various ways to take advantage of strong demand for Covid-19 vaccines.

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The scams are just the latest instances of people seeking illicit gains during the pandemic in India. During the Covid-19 surge in April and May, many people had to pay high prices for oxygen and antiviral medications on the black market when they weren’t available through authorized distributors. Authorities say the scarcities were in part caused by people hoarding and reselling on the black market. In early May, for example, as hospitals were struggling to get oxygen supplies, police in New Delhi raided a building and seized more than 400 oxygen concentrators.

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India has put vaccine distribution to other countries on hold as the country battles the world’s fastest-growing Covid-19 surge. The delay in distribution is hampering the global vaccination effort. Photo illustration: Laura Kammermann The Wall Street Journal Interactive Edition

“They are playing with people’s lives. I don’t know what has happened to people. They are not even sparing this pandemic to make profit,” said Hitesh Patel, 42, who was one of the residents in the housing complex who got a shot that police say was fake.

Mr. Patel’s housing complex was one of 10 sites in the Mumbai area where fake vaccination drives were held, with about 2,500 people falling victim, police said.

Police have arrested 14 people for their alleged involvement, including two doctors at a local private hospital, and charged them with culpable homicide and criminal conspiracy, said Vishal Thakur, Mumbai’s deputy commissioner of police who is heading a special team investigating vaccination scams in the city.

At the housing complex, someone posing as a representative from a local hospital reached out to the residents’ welfare association for the development, offering to set up the vaccination drive, according to Mr. Thakur and residents there.

The association agreed, and on the morning of May 30, six people showed up to administer the purported vaccines, including three dressed in nurse uniforms. They spent about three hours there administering the fake vaccines and recording the personal information of the nearly 400 residents, domestic helpers and drivers who had signed up, with each paying about $17 to receive the doses. Domestic workers in India usually earn less than $70 a month.

Residents said some of them became suspicious when the people administering the illicit vaccines entered the details in a spreadsheet, rather than the government app for tracking vaccinations, called CoWin. “Later many of us checked the CoWin app, but there was no record of our vaccination. None of us also experienced any post vaccination symptoms. It was definitely not a coincidence,” said Mr. Patel.

In the eastern city of Kolkata last month, more than 500 people were injected with a substance they thought was Covid-19 vaccine. Instead, forged vaccine labels were stuck on used vials that contained Amikacin Sulphate, an antibiotic used to treat serious infections, authorities said. So far, nine people have been arrested, including a man accused of posing as a civil servant to organize the vaccination.

“Such incidents have left people shaken. Those injected with the so-called vaccines are now panicking about the possible side effects,” said Atin Ghosh, a health official in Kolkata’s municipal corporation.

In New Delhi, police arrested two men in late May for allegedly creating at least five fake Covid-19 vaccination websites, luring thousands into paying registration fees of up to $26. The layout of the websites mimicked the government’s CoWin site, a New Delhi police officer said.

Experts say black markets for fake and illicit pharmaceuticals have long been a problem in the developing world, but the scarcity of vaccines when highly contagious Covid-19 variants are spreading is creating an opening for those who want to exploit the situation. “The vast majority of vaccines are legitimate and a lot of work lies ahead in stamping out the problem of fake, illegitimate vaccines,” said Ramanan Laxminarayan, an epidemiologist at the Center for Disease Dynamics, Economics and Policy.

The scams are the latest setback to India’s effort to vaccinate its more than 1.3 billion people against Covid-19. In March, the country halted vaccine exports from manufacturers, including the world’s largest, the Serum Institute of India, because of insufficient supplies. When the country expanded vaccine eligibility to all adults on May 1, many states reported shortages of supplies and many people said they were unable to book appointments.

The campaign has accelerated in recent weeks, as the federal government assumed greater control of vaccine procurement and distribution. With 6.3% of the population fully vaccinated as of July 20, according to Our World in Data, a project based at Oxford University, the country has a long way to go to meet its goal of immunizing every adult by the end of the year.

Anita Shekhar Castellino, a Mumbai-based lawyer who has filed a public interest lawsuit on fake Covid-19 vaccinations in the Mumbai High Court, said scams threaten to shake people’s faith in the safety of shots at a critical point in the country’s immunization campaign. “A lot of people, who were keen to take the vaccine, might become reluctant again for fear of getting injected with something unknown. It could build up [vaccine] hesitancy,” she said.

Write to Vibhuti Agarwal at vibhuti.agarwal@wsj.com