Thousands rushed to a station in India's western Gujarat state to greet Khan, who was making brief stops on his journey to Delhi to promote his latest film "Raees" ("Wealthy").
But the excitement turned to panic as fans were crushed trying to catch a glimpse of the Indian screen icon, who waved briefly from a passenger door.
Amid the stampede 45-year-old Farid Khan Pathan fell unconscious and collapsed, later dying in hospital.
Shah Rukh Khan takes son AbRam's help to promote Raees
India's railway minister Suresh Prabhu said on Twitter he had ordered police to "investigate the matter and take stern action against any lapse".
Television footage showed swarms of people running towards Khan's carriage, elbowing one another to take pictures with smartphones as baton-wielding policemen tried to control the swelling numbers.
Two officers were also injured trying to bring order to the chaos, said Sharad Singhal, a senior railway police officer.
He said police were establishing whether the film organisers had sought permission before staging the stunt.
Mahira Khan ups the style quotient with Raees promotions
"We will investigate whether police failed to do its part or the organisers did not comply with rules and regulations," he told reporters.
"We will take action against all those who were responsible, even if it was Shah Rukh Khan."
The 51-year-old film star offered his condolences as news broke of the man's death.
"It is extremely unfortunate that someone has died... my prayers are with his family," he told reporters as he approached Delhi.
"I hope his soul rests in peace and his family remains well."
"Raees", a crime-thriller set in the 80s about the rise and fall of a clever bootlegger, hits Indian cinemas this week.
Epic Madness at #SURAT Railway Station for #Raees Bhai 😊 @iamsrk @RaeesTheFilm @ritesh_sid #RaeesByRail #ShahRukhKhan #Srk @RedChilliesEnt pic.twitter.com/OBDEJQPpZU
— Jaey Gajera (@JaeyGajeraIndia) January 23, 2017
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