The Press Trust of India reported officials at the Vadodara railway police control room as saying, "At around 10.30 PM the train arrived at platform number six of the station and halted for 10 minutes."
PTI added that the crowd went berserk after the train pulled in and began banging on its windowpanes.
It added that some people ended up falling on top of each other, and that police had to resort to a mild lathi charge to control the crowd.
The deceased was identified as Farheed Khan Pathan, a local politician.
Local media reported that as Khan's train pulled out of Vadodara -- he was on his way from Mumbai to Delhi -- the assembled crowd rushed for the exits, leading to a stampede.
A number of people fell in the ensuing chaos, including Pathan.
On reaching Delhi, Khan told reporters: "It is extremely unfortunate that someone has died... my prayers are with his family."
He added that members of his team were at the deceased's funeral.