Benjamin Medrano said his sexuality only became an issue in the electoral campaign when the opposition tried to use it against him in conservative Zacatecas state.
The city has been caught up in a turf war between drug cartels operating in central and northern Mexico.
Mr Medrano says he hopes to make a difference for the people of Fresnillo.
He posted a message on his Twitter account soon after the ceremony: "The time has come to listen to your demands and address your problems. I have a commitment with you".
Two of Mexico's biggest criminal organizations - Los Zetas and the Gulf Cartel - have been fighting for control of drug trafficking routes leading north towards the American border.
Mr Medrano said the fact that he has no involvement with criminal organisations would enable him to do a good job for the people of Fresnillo.
"What matters the least for the people is who you may sleep with, what you do in your private life. What they want is good results from their politicians," he told BBC Mundo.
Gay marriage
Mr Medrano comes from a very poor background in Zacatecas state. He went to the United States aged six, as part of an "artistic caravan".
He returned to Mexico after many years to finish school and to read law at university.
He began a professional career as a singer and opened Fresnillo's first gay nightclub.
A Roman Catholic in a very conservative part of Mexico, he says he has no intention of getting married.
He denied being against gay marriage, but hinted that what is acceptable in the capital, Mexico City, and other regions of the country may not be acceptable in Zacatecas.
"My agenda is based on achieving human and social development for all of us who live in Fresnillo, regardless of sexual orientation," he told BBC Mundo.
Security is the main concern of the population of Fresnillo, a city of some 200,000 inhabitants.
"First, we need to get our police better equipped and better trained, so they don't become accomplices of the criminal gangs," said Mr Medrano.
He was elected mayor for the centre-right Revolutionary Institutional Party (PRI) of President Enrique Pena Nieto, who took office in December promising to review the "war on drugs" policy of his predecessor.
BBC