"Aligarh" is based on the real life incident of Srinivas Ramchandra Siras, an academician at the Aligarh Muslim University who was suspended from his job because of his sexual orientation.
According to reports, a fringe group called the Millat Bedari Muhim Committee (MBMC) has pressurised exhibitors in the city not to screen the film.
Aligarh Mayor Shakuntala Bharti also reportedly supported the group's call for a ban on the film.
"It doesn't seem like an official ban. The mayor has joined the issue with a fringe group (MBMC). Our stand is the city of Aligarh has, once again, killed professor Siras," Mehta told IANS.
Mehta said he is discussing the issue with his legal team, but he cannot do "anything that will create a law and order situation".
The fringe group also reportedly wrote a letter to the information and broadcasting ministry.
Calling the group "homophobic", Mehta said it is "just seeking attention".
"They are homophobic. Their worry is that Aligarh, which is famous for knowledge and its locks, will be linked only to homosexuality with this film. There can't be any more homophobic statement than this," Mehta asserted.
"Aligarh" also stars Rajkummar Rao. The film released on February 26.