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