All vaccines will be available during regular clinic hours in Henry, Shelby, Spencer and Trimble counties.
The governor introduced the incentive as a way to get more people vaccinated against COVID-19.
At random, two kids will be assigned to get the Pfizer vaccine for every one child who gets a placebo.
UofL Health announced in May that it would require all employees to get vaccinated, starting Sept. 1.
Humana and Volunteers of America have partnered to create the Determined Health program.
There are at least seven upcoming mobile events beginning Thursday, June 24 where people can go to get a vaccine.
Children from ages 6 weeks to 12 years old can be dropped off, no reservations required, for a maximum of two hours at one of the participating branches.
The milestone comes just days before the commonwealth relaxes capacity restrictions and ends its curfew on bars and restaurants.
The statewide rate of positive cases was 2.61% as of Monday.
The commonwealth's positivity rate rose slightly from 2.63% on Saturday to 2.64% on Sunday.