Ospreys flanker Jonathan Thomas also picked up an injury (dead leg) at the weekend and he will be further assessed on Thursday for his availability to feature against Ireland.
Rees has a slight hamstring problem which is currently hampering his preparations and he joins James Hook (calf), Ryan Jones (calf) and Morgan Stoddart (shoulder) on a list of players who have been managing issues around training during the early part of this week - although all are also expected to be available.
"Both Matthew and Morgan have responded well to extensive treatment since picking up their injuries against Italy," said Wales national performance medical manager Prav Mathema.
"Matthew has a slight hamstring problem and Morgan sustained an injury to his shoulder during that match, but the medical staff has managed both players very well and together with the hard work they have put in so far we expect both to be available for Ireland.
"Richard has a shoulder problem sustained during his outing for the Ospreys this weekend and he needs rest at the moment although he too should be okay for Saturday. Jonathan also picked up his injury at the weekend and we will further assess him towards the end of this week.
"The issues with Ryan and James just mean they have taken a limited part in some sessions so far during our preparation but, again, both will be fine."