Warren Gatland's men will head across the Atlantic for a Test match against South Africa in Washington DC on June 2 before moving on to Argentina for a two-Test series with the Pumas.
Gatland named his squad for the trip nine days ago but has now been forced to make changes, with Josh Adams, Tomas Francis and Luke Charteris, who all ply their trade in the Aviva Premiership, unable to feature in the clash with the Boks.
The encounter falls outside the World Rugby Test match window and, with the trio having not been given permission to feature, Gatland has decided he wants players who will be available for the entire tour.
Uncapped Dragons pair Ashton Hewitt and Aaron Wainwright have been called into the squad along with Ospreys prop Rhodri Jones.
"We are really disappointed that Josh, Tomas and Luke have to miss out on the opportunity to tour with Wales and play international rugby this summer," Gatland said.
"It was a great opportunity for them to play for their country, press their claim in an important year, and it is a shame supporters will not get to see them in the red of Wales."
Cardiff flanker Navidi has also been ruled out of the summer tour after he suffered a dislocated shoulder in the Blues' Challenge Cup final win over Gloucester on Friday.