The 24-year-old suffered the problem during a morning session at Melwood.
Some earlier reports on Wednesday had suggested the Senegal international might have dislocated his shoulder.
Mane signed from Southampton in the summer for £34m and scored on his Liverpool league debut during Sunday's 4-3 win at Arsenal.
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Liverpool forward Sadio Mane is a doubt for Saturday's Premier League match at Burnley after suffering a muscle injury in training.