Soham Mukherjee, a second year student of post graduate programme hailing from Kolkata, was found hanging from his hostel room, they said.
As the room was locked from inside, the police prima facie was taking it as a case of suicide but no note has been found, the police said.
Mr Mukherjee was an engineering graduate from Indian Institute of Technology (IIT), Guwahati, and worked for a multi-national firm for a couple of years before taking admission in the IIM, Lucknow last year.
The police has seized laptop and mobile phone of the victim and are trying to get more details, they said.
Initial probe suggested that the victim was under depression may be due to some personal problem as he was not attending his classes since November 12 and was not picking up his classmates and other hostel mates' calls since morning, the police said.
The exact motive behind the suicide could not be ascertained yet and further probe in on in the matter, the police said.
The victim's family, staying at Jodhpur Colony of Kolkata's Lake Garden area, have been informed, they said, adding the body has been sent for post-mortem examination.
The IIM administration expressed grief on the student's death and a press communique from the IIM read that he was a consistently well performing student.
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.