Wildlife activists say the bill violated the federal Endangered Species Act.
In her veto letter, Brewer said she is a strong supporter of states' rights but feels the bill is unnecessary and conflicts with federal law.
"A state simply does not have the power to allow a take on federal lands," Brewer wrote.
A separate bill approved by both chambers sets up a reimbursement fund for ranchers who lose cattle to wolves. It still requires final action.
Proponents say the federal government is overstepping its boundaries with its wolf-recovery program in Arizona and New Mexico.
Brewer vetoed the bill on Tuesday.