The stampede at Sandhya Theatre on 4 December left a woman named M Revathi dead and her child injured.
Revathi, 39, was attending the screening with her husband M Bhaskar, their son, and seven-year-old daughter.
Arjun, 41, arrived at the theatre at around 9.30pm local time, entering through the main entrance and spending 15-20 minutes outside, NDTV reported.
As news of his presence spread, hundreds of fans gathered to catch a glimpse, causing the gates to collapse. Attempts by his security team to push the crowd back reportedly only exacerbated the situation.
Police filed a case against Arjun, his security team, and the theatre management, citing a lack of crowd control measures and charging them with culpable homicide not amounting to murder and voluntarily causing hurt, Akshansh Yadav, deputy police commissioner, told The Indian Express.
The Telugu language film actor moved the Telangana High Court on 11 December requesting the case be quashed. He was arrested before his plea could be heard on Friday afternoon.
In the wake of Revathi's death, the film's producers, Mythri Movie Makers, expressed condolences and pledged support for her family.
"We are extremely heartbroken by the tragic incident during last night's screening," they said in a statement. "Our thoughts and prayers are with the family and the young child undergoing medical treatment.
"We are committed to standing by them and extending all possible support during this difficult time. With deep sorrow."
Arjun expressed grief over Revathi's death and promised Rs 2,500,000 (£23,300) to the victim's family. He also promised to cover the medical expenses of the injured son.
"A very unfortunate incident took place at Sandhya cinema. We are extremely sorry for that," he said at a success party for the film on 7 December.
"When I heard about it on December 5, I was in shock. It took me hours to process it and respond to the incident. I couldn't process it psychologically. It took me around 10 hours. We all blanked out when we heard the news. Sukumar got extremely emotional." Sukumar is the director of Pushpa 2.
Arjun reportedly complied with his arrest on Friday morning but told police he felt uncomfortable about them entering his bedroom without notice. The actor reportedly could not change or finish breakfast before being taken into police custody.
His father, producer Allu Aravind, accompanied him to the local police station.
After giving his statement, Arjun was driven to Osmania Hospital for a check-up and was scheduled to be presented in court later.