Number eight Wainwright was injured early in Friday's 43-0 hammering by France in Paris. Wales are waiting for the results of a scan but there are fears the 27-year-old may have suffered a broken cheekbone.
Ospreys centre Owen Watkin is being assessed after sustaining a knee injury.
Sale prop WillGriff John has rejoined the squad in Nice, where Wales are based ahead of their second Six Nations game in Rome.
John failed a head injury assessment in Sale's defeat by Bath in the English Premiership last week.
Wales' defeat against France was a 13th successive Test loss and they failed to score in a Five Nations or Six Nations game for the first time since 1998.
Warren Gatland's team finished bottom of the table in 2024, losing all five of their matches.