The England ace has had a difficult season on the injury front but having got back to full fitness recently, the 31-year-old suffered a new setback after picking up a hamstring strain while on international duty.
Gerrard, having being overlooked for the captain's armband, suffered the injury in the first half of England's 3-2 defeat to the Netherlands at Wembley on Wednesday night and had to be taken off.
Persistent injuries of late was perhaps one of the reasons caretaker England manager Stuart Pearce decided to appoint Scott Parker as captain but Dalglish has revealed that the latest problem is not too serious.
The Reds boss also confirmed that Glen Johnson was left out of the squad beaten 2-1 by Arsenal on Saturday as a precaution and should also return to the fray soon, although Daniel Agger is expected to be out for some time with a broken rib.
On Gerrard's injury, Dalglish told the club's official website: "It won't be long, and Glen Johnson was out as a precaution as well. Daniel Agger is out with his ribs and Daniel is the one who'll be out longest out of the three lads."
The weekend defeat has left the Reds 10 points behind fourth-placed Arsenal, although Liverpool do have a game in hand, and will travel to Sunderland next Saturday before the derby game at Anfield the following Tuesday.