The 23-year-old victim was attacked in the early hours of Tuesday after he left an Asda store in Colindale just an hour and 20 minutes after the notoriously violent game went on sale at midnight.
He was hit with a brick, stabbed and stripped of his mobile phone, watch and his copy of GTA V near the supermarket.
The three males – aged 15, 17 and 18 – are being held on suspicion of robbery at a north London police station.
The victim is now recovering in hospital, where he is said to be in a stable condition.
A Metropolitan Police spokesman said: “The motive for the attack is unclear at this stage.
“The victim had been shopping and was on his way home when he was hit with a brick.
“He was then stabbed and robbed.”