The incident occurred on Sunday at a primary health center in Yavatmal during the National Polio vaccination campaign against polio, said Shrikrishna Panchal, a senior official on the Yavatmal District Council.
The incident was revealed after one of the children complained of malaise and vomiting, Panchal told CNN.
All of the children were admitted to the district Government Medical College and are in stable condition, the official said.
An investigation was ordered against the three health workers, including a doctor, who was present at the time of the incident, he added.
On Sunday, the Ministry of Health and Family Welfare of India started a three-day polio vaccination campaign in India.
Polio was once a common virus. In some children, it can affect nerves and cause muscle weakness or paralysis. There is no treatment or cure, but vaccination can prevent infection.
In 2014, the World Health Organization certified that India was free of polio after three years without an endemic case.
Five years earlier, India was home to almost half of global polio cases and was considered one of the most technically difficult places to eradicate the disease, due to the challenges of sanitation and high population density.
Polio eradication in India has been heralded as one of the greatest achievements in global health efforts, but vaccination and surveillance programs must continue to prevent outbreaks.
Polio has been eradicated in Southeast Asia, the Americas, Europe, most of Australasia and Africa. Wild polio strains now circulate in only two countries: Afghanistan and Pakistan.