Pravin Gopaldas Joshi, 20, sprinkled petrol on himself and lit a match at 5.30 p.m. in the men's restroom in the Amber cinema of Jamnagar, about 400 km from here.
People in the cinema house, however, doused the fire and rushed him to the Guru Gobindsingh hospital, police said. He suffered 70 percent burns, according to doctors.
Joshi, a resident of Rajkot in Saurashtra, had gone to Jamnagar to apparently lodge his protest against the only cinema house in Gujarat screening the movie.
The youth wing of the ruling Bharatiya Janata Party (BJP) has called for boycotting the film after Khan expressed solidarity with the Narmada Bachao Andolan that is fighting for the rights of the people displaced by the Sardar Sarovar dam on the Narmada river in the state.
The project is seen as a lifeline for the drought-prone parts of the state.
"Aamir must apologise for remarks. I appeal to the people of Gujarat to boycott his film till he tenders his apology," Joshi told a news channel from the hospital.
Meanwhile, BJP activists in Surat in south Gujarat disrupted a private screening of the film, released in the rest of the country last month.