"Mark has undergone a minor surgical procedure following a scan on Monday," said Wales team physio Mark Davies.
"He is ruled out of contention for this weekend's game, but is expected to make a speedy return to action."
Injuries have seriously undermined Wales' Six Nations title defence and they end the season without 11 key players, including six of last summer's British & Irish Lions.
Caretaker coach Scott Johnson insists he is a "glass half-full man" and attempts to put a positive spin on the catalogue of injuries by declaring it will leave Wales in a much stronger position at the World Cup.
But the immediate affects have been painful. A year ago Wales sparked the mother of all parties with a Grand Slam-sealing victory over Ireland.
This Saturday, if they lose to France and Italy beat Scotland, then Wales could end their title defence with the wooden spoon.
Defence coach Clive Griffiths admitted this week: "Last year we had all the luck and all the play. This year we have had disastrous luck with injuries.
"It's not our year. It would have been a magnificent achievement to have back-to-back Grand Slams or championships.
"Last year does seem a long time ago. But that's sport - you only have to look what's happened with English cricket.
"They have had the highs of the Ashes and now they are experiencing the lows in Pakistan and India. It's after the Lord Mayor's Ball. It happens."