Youngs started England's opening Six Nations match against Italy on Sunday but was forced off in the first half after suffering knee ligament damage and there are fears he could be ruled out for the rest of the tournament.
The Leicester scrum-half is set to undergo scans to determine the full extent of the injury and an update is expected from the Rugby Football Union late on Monday or Tuesday morning.
Wigglesworth has plenty of experience, having played in two World Cups, and he will be hoping to earn his 28th international cap in Saturday's clash with Wales, who thumped Scotland in their first Six Nations match.
However, Danny Care is expected to start in the number nine jersey against Warren Gatland's men at Twickenham, having stepped off the bench to replace Youngs at the weekend in the convincing 46-15 win over the Azzurri.
England have also added Exeter hooker Luke Cowan-Dickie to the 32-man squad while Wasps No 8 Nathan Hughes will join the camp to assess when he will be available for selection after being out injured with a knee injury since December.