Yolanda Sánchez was shot in the town of Cotija, which she had governed since September 2021.
She was the first woman to be elected to the post.
Widespread violence against politicians has overshadowed Mexico's general election, which saw two women run for the presidency.
Yolanda Sánchez was ambushed by gunmen in the centre of Cotija, Michoacán, on Monday.
Local media say she was shot 19 times and died in hospital shortly after the attack. Her bodyguard was also killed in the gun battle.
No arrests have been made so far in connection with the attack but it is widely thought that the gunmen belonged to an organised crime group.
Ms Sánchez had reported receiving death threats after taking up office in September 2021.