The actor, who was convicted last month for illegally possessing weapons in a case linked to the 1993 blasts in Mumbai, was meant to return to prison by tomorrow.
On Monday, he applied for six months before he began his prison sentence. His lawyers had said he would like to shoot for seven movies in which nearly Rs 280 crores are invested.
"We extend the time by four weeks from tomorrow. It is made clear that no further extension will be granted," the judges said.
The CBI had argued against Mr Dutt, arguing that "the floodgates would open" for appeals by other convicts if the deadline for his imprisonment is extended.
The Supreme Court last month sentenced Mr Dutt to five years for possessing firearms supplied by men who executed the bombings in 1993 that killed more than 200 people in Mumbai.
Mr Dutt had already served 18 months of his sentence but was released on bail while his case was appealed. He now has to serve the remaining three-and-a-half-years of his term.
At an emotional press conference last month, he had said he would not appeal against his sentence.