Dutt was granted leave of furlough for 14 days by the prison authorities, Yerawada jail superintendent Yogesh Desai told PTI.
Good conduct is one of the criteria for granting furlough, which is sanctioned from prisoner's accumulated leave, Desai said.
Later, talking to journalists who had gathered outside his Bandra home, Dutt pleaded for privacy, saying he had little time to spend with his family.
Dutt, 53, is serving the remaining 42-month jail term for possessing illegal firearms, part of the cache of weapons which were supposed to be used during the 1993 bombings.
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He was shifted to Yerawada jail from Mumbai's Arthur Road Jail on May 22 in a hush-hush pre-dawn operation.
In its March 21 verdict, the Supreme Court had reduced Dutt's jail term from six years to five. The actor had already served 18 months behind bars.