He felt a problem after coming on as a second-half substitute at St James' Park and a scan showed a strain.
It is the latest in a long line of injury absences for the 26-year-old, who had just returned to action after knee and foot problems.
Sturridge has made six appearances so far this season, scoring four goals.
Having scored 28 times for Liverpool and England in 2013-14, he was restricted to just 18 appearances last season because of thigh, calf and hip injuries.
After recovering from a hip operation in May, Sturridge played three games at the start of this term but then did not feature from 4 October until 29 November.
He scored twice in the 6-1 League Cup quarter-final win at Southampton last Wednesday but was hurt at Newcastle after coming on in the 62nd minute.
When a foot problem picked up in training forced him to miss the Reds' Europa League win over Bordeaux on 26 November, Liverpool boss Jurgen Klopp said Sturridge had to learn "what is serious pain and what is only pain".
Liverpool, currently eighth in the Premier League, face seven games from now until the first leg of their League Cup semi-final at Stoke on 5 January.
Liverpool striker Daniel Sturridge will be out for several weeks after suffering a hamstring injury during Sunday's defeat by Newcastle.