Thatcher was ruled out of the recent friendly with Slovenia in Swansea with the same problem but has played in City's first four games of the season, aggravating it in Saturday's win against Portsmouth.
The FA of Wales had threatened to report City to FIFA over their refusal to allow Thatcher to travel to Cardiff to have his ankle injury assessed by the Welsh squad's medical team.
But after Wales boss John Toshack discussed the situation with City chief Stuart Pearce and the player, Thatcher will now be examined by a Wales surgeon at a Manchester hospital on Friday afternoon.
A City spokesperson said: "It was felt that it would be wrong to ask Ben to drive to Cardiff with an ankle injury, so now a compromise has been reached that a surgeon will examine him in Manchester."
FIFA regulations state that clubs cannot stop a player being called up for international duty regardless of whether he is injured or not, otherwise the player can be banned from playing for his club for the next five days.