Activists of an NGO administered the vaccine to 24 children yesterday and of them 15 developed complications like vomiting and fever.
They were rushed to the taluk hospital and three died today, police said.
Those who were suffering from complications are undergoing treatment, District Health Officer Dr Srikant Basur said.
The deceased were in the age group of 18 months and two years.
Following the death of their children, their parents lodged a police complaint and a FIR has been registered, police said.
Hospet Taluk Assistant Commissioner D R Ashok Kumar banned the activities of the private NGO and directed it not to continue with the vaccination programme till further orders.
Tourism Minister Anand Singh ordered an inquiry into the deaths and announced Rs 50,000 compensation to each of the bereaved families.
Government will meet the treatment expenses of other children undergoing treatment in hospitals, he said.