The flanker sustained the problem during his nation's 67-14 victory over Italy on March 19.
Tipuric's club Ospreys have announced that the 26-year-old has been advised to spend the next three months away from the game.
A statement read: "Justin is recovering well following the concussion suffered playing for Wales against Italy three weeks ago, but in the light of his symptoms the specialist advice is that it is in his best interests to take his time returning.
"A prolonged three-month period of recovery rules him out of the rest of the season for the Ospreys and the Wales tour to New Zealand. The focus for Justin will be on getting healthy and fit, ready for pre-season."
Tipuric is also unlikely to be selected for Great Britain Sevens at the Olympics in Rio this summer.