The Uruguay international had been set to step up his preparations for the new season when the Reds take on Valerenga on Wednesday, but will instead have a scan on his foot to assess the extent of the injury.
Suarez has been the subject of a £42 million bid from Liverpool's top-four rivals Arsenal this summer, though it was rejected by the Merseyside outfit who are adamant the Uruguayan is not for sale.
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Suarez and his representatives are also reported to be contemplating taking legal action against Liverpool, after believing he had the option to join Arsenal after they matched his alleged buy-out clause.
Liverpool boss Brendan Rodgers has recently hit out at his managerial counterpart at Arsenal, claiming the club have lacked class in their pursuit of the forward.
A number of other first-team squad members miss the trip to Norway including defensive trio Glen Johnson, Daniel Agger and Martin Srktel.
Suarez becomes the latest high-profile transfer target to pull out of a pre-season fixture through injury. Wayne Rooney has yet to feature in pre-season, and will be absent from Manchester United's latest game against AIK Fotboll (which can be watched here), while Tottenham's Gareth Bale missed Spurs' 5-2 defeat to Monaco.
Liverpool squad in full:
Jones, Enrique, Toure, Alberto, Gerrard, Aspas, Coutinho, Assaidi, Henderson, Coates, Downing, Spearing, Lucas, Mignolet, Allen, Borini, Sterling, Kelly, Flanagan, Ibe, Wisdom