House Bill 1 would gradually raise it from $7.25 to $10.10.
The vote Thursday was 54 to 44.
Minimum wage in Kentucky has been $7.25 an hour since 2007.
Under the proposal, it would go up to $8.20 on July 1, 2014.
The legislation would them raise the wage each year until it is $10.10 in July of 2016.
House Republicans against the change pointed to a study that said a minimum wage increase would cost the state 14,000 jobs.
The bill now goes to the Republican-led Senate.