Gisela Mota was killed at her home in Temixco, 50 miles south of the capital Mexico City, hours after taking her oath of office on January 1, police said.
Reports said Gisela Mota, a former federal congresswoman, was attacked by four gunmen. Police shot two of the attackers dead and arrested the others.
A motive for the killing is unclear. Several Mexican mayors were killed in 2015 by alleged drug traffickers.
Gisela Mota, who was in her early 30s, had promised to try to clean up Temixco, an industrial city where problems associated with drugs and organized crime are rife.
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