The incident took place in a school in Sagar district where children were being given Covid-19 vaccines.
India's health ministry mandates a "one needle, one syringe, only one time" protocol for Covid-19 vaccines.
India has administered over 2.03bn Covid-19 vaccines so far.
Single-use disposable syringes are widely used in India to avoid the spread of deadly diseases like HIV. However, there have been multiple incidents in the past where a single syringe has been reused in hospitals due to a shortage of equipment.
Jitendra Rai, who was vaccinating the children, told the media that he was only given one syringe by the health department and he was just following orders.
Parents who had accompanied their children spotted the issue and reported it to the school authorities.
When state officials reached the school, Mr Rai was missing from the school and his phone was turned off.
The state's health department has registered a case of negligence against him. Meanwhile, it has also started an inquiry against the official responsible for dispatching equipment for the vaccination drive.
A spokesperson from the opposition Congress party has demanded that the state's health minister should resign over the incident.
India is the second country after China to have crossed the two-billion Covid vaccines mark. In July, the government announced a 75-day free Covid booster dose programme for all adults to mark India's 75th independence anniversary.
According to India's health ministry, 98% of adults have received at least one dose of the Covid vaccine, while 90% have been fully vaccinated.
On Wednesday, the country reported 18,313 daily cases for the past 24 hours and 57 Covid-related deaths.