Kaufert has served as state representative since 1990, including a stint as co-chairman of the Joint Finance Committee.
The 56-year-old Kaufert said earlier this week he's leaning toward finishing his term in the state Assembly. His legislative term ends in January.
Kaufert is the 10th Assembly Republican who will not seek re-election. Six Democrats are also not running again for the 99-member Assembly.
Republicans hold a 60-39 majority in the Assembly.