Wales play South Africa in Washington on June 2, a date that falls outside World Rugby's official window and Premiership Rugby Limited says the players are ineligible to play in the game.
"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," Wales coach Warren Gatland said.
Lock Charteris, prop Francis and winger Adams are eligible to take part in tests in Argentina on June 9 and 16 but Wales need their players to be available for the whole tour.
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"The situation is very clear for players playing in England going forward and heading into a Rugby World Cup year," Gatland said.
"With the players unavailable to link up with the squad until the week of our second test match, we have had to replace them in the squad."
Prop Rhodri Jones and the uncapped Ashton Hewitt and Aaron Wainwright have been called up to replace them.
Flanker Josh Navidi has been ruled out of the tour after dislocating his shoulder playing for Cardiff Blues in their European Challenge Cup final win over Gloucester on Friday.
(Reporting by Ed Osmond, editing by Pritha Sarkar)
