The 26-year-old received a torrent of criticism on Twitter after he posted a picture of himself 'blacked up', wearing a straw hat and claiming to be a sunglasses salesman.
Alongside the picture - posted to his Instagram and Twitter accounts - he included the caption: "Great Xmas do with the boys.. level - fancy dress - completed."
After initially making light of the criticism, Norwood went on to admit that he had made a mistake and said: "I would like to apologise for any offence I have caused, it was certainly not intentional."
A Rovers spokesman said: "It was an error of judgement rather than an intention to be racist or cause offence and James has apologised for his actions. The squad were booked on to a PFA Equality and Diversity workshop on Tuesday which they are taking part in today. The club will be making no further comment."
Norwood has notched up 28 goals in 51 league appearances since his arrival at Tranmere in summer 2015.