Cuthbert, who played an influential part in the 24-6 victory (including scoring the opening try), is set to be sidelined for up to six weeks.
“Alex has been in excellent form leading into this tour – and it was there for all to see at Eden Park on Friday – so it’s a shame he’s had to leave us at this juncture,” says Wales head coach Robin McBryde.
“He’s also been a great influence off the field with the younger players in the squad. I know he’ll work hard now to be back in action for Cardiff Blues’ pre-season.”
Wales will be making no call-ups at this point as they prepare to face Samoa in Apia this Friday (23rd June).