Dutt will be soon shifted to to Pune's Yerawada Jail to complete his prison term.
He has been lodged in the transit barrack of the high security prison.
After arriving at the jail at around 11 PM on Thursday night, Dutt was reportedly escorted to his room.
He ate home-cooked food for dinner and lay down to sleep. He wanted a bottle of water, which was provided to him, reports said.
However, he was seen changing postures all through the night and even woke up and sat a few times, media reports said.
On Thursday, the actor had left his Mumbai home to serve his jail term.
He was seen accompanied by his wife Manyata and filmmaker Mahesh Bhatt.
Though Dutt earlier said he feared for his life from fundamentalists and would surrender at Yerwada Jail in Pune, he later chose to surrender in the TADA court.
On Wednesday, authorities at the Arthur Road Jail received an anonymous letter stating there is a threat to the actor's life inside the prison premises.
The Police said he will be given adequate protection.
Earlier, the Supreme Court ruled out any extension of surrender time to Dutt in the 1993 Mumbai blasts case.
The apex court refused to accept the appeals filed by producers of Dutt's films under production.
The Supreme Court on Apr 17 last gave four weeks more to Dutt to surrender before the law and go to jail to serve his term after his conviction in the 1993 Mumbai bomb blasts case.
On May 10, giving a blow to Dutt, the Supreme Court rejected his plea that sought review of its March 21 decision where he was convicted in connection with the 1993 Mumbai serial blasts case.
The Supreme Court on Mar 21 announced its verdict on Dutt for illegal arms possession during the Mumbai bombings that had killed 257 people in 1993 in the nation's financial hub.
On Mar 12, 1993, twelve coordinated blasts in Bombay Stock Exchange, Air India Building at Nariman Point and hotels Sea Rock and Juhu Centaur resulted in death of at least 257 people and injury to more than 700.
It was alleged that the blasts were the instruments to avenge the demolition of the Babri mosque in Ayodhya in December 1992 and were allegedly conspired by underworld don Dawood Ibrahim (believed to be hiding in Pakistan now) and two other terrorists-Tiger Memon and his brother Yakub Memon.