Gisela Mota formally took office with the new year on Friday. Mexico City newspaper EL Universal said she was attacked at her home by four armed gunmen.
Local police later arrested two alleged attackers, while killing two others, according to a statement issued by the Morelos attorney general's office.
The statement did not provide further details of the attack.
Several mayors were killed last year in Mexico, where armed gangs financed by the drugs trade control many local communities.
Temixco, located some 60 miles (100 km) south of Mexico City, has a population of about 100,000.
Mota, a former federal member of Congress, belonged to the leftist Party of the Democratic Revolution.
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