"He was examined by doctors and will be absent from training", the club said in a statement, explaining that his admission to the hospital was "a precaution".
The German had to cancel his appearance at the premiere of the movie, "Kenny" - A Tribute to Kenny Dalglish, who now has a stand named after him at Anfield.
Meanwhile captain Jordan Henderson has declared himself fit after a similar problem caused him to miss the Premier League win over West Ham before the global break and England's two friendlies against Germany and Brazil. That forced him to miss a first-team training session.
Reds captain Henderson was unavailable for the 4-1 rout of West Ham before the worldwide break with a thigh complaint, and was absent for England's friendlies against Germany and Brazil as a result.
Mane initially returned to Melwood on Tuesday but spent two days in rehab before joining up with the rest of the squad in full training this afternoon.
Fellow midfielder Lallana has not played since August after damaging his thigh, and has been working on an individual programme.