The 23-year-old Murphy scored a scintillating try and was voted man-of-the-match in Munster's 31-9 European Cup pool win against Premiership leaders Sale on Saturday.
Full-back Dempsey, who has been in sensational form for Leinster this season, took a knock to his calf in his province's European Cup win over Bath at the Rec on Sunday, and was not available for training with the Irish squad on Monday. The injury will be assessed by the Ireland medical staff over the coming days.
O'Sullivan's 35-man squad for the forthcoming RBS 6 Nations championship assembled at a south Dublin hotel on Sunday night after their European Cup exertions.
In addition to Dempsey's injury, a total of 17 players were unavailable for training on Monday due to various minor injuries, forcing O'Sullivan to cancel a planned session in the afternoon.
O'Sullivan said: "Although none of the injuries are a major fitness concern, given the fatigue levels after the weekend, there is no benefit to be had from training.
"The players will need some time to recover from what was a tough but hugely successful weekend for Ireland in Europe. The extra day's rest will allow the players to recover sufficiently to hit the ground running on Tuesday."
Commenting on the inclusion of youngster Murphy, O'Sullivan added: "Barry has shown significant improvement with every game he has played this year with Munster. His call up to the national squad is due reward for his performances to date."
Murphy has played in all six of Munster's European Cup games this season, starting three games against Sale (2) and Castres. A former Ireland Under-21 international, he made his Munster debut against the Dragons in the Celtic League in 2003.
Ireland open their RBS 6 Nations account against Italy at Lansdowne Road on February 4.