The 26 year-old, who controversially declared himself eligible for the national side last season despite previously representing New Zealand, is currently in talks with NRL outfit St George over a possible move.
However, the 2011 Super League Man of Steel could be forced to stay at the Tigers, with legal teams investigating contract disputes between agents.
“It is a great shame that Rangi will miss the matches against France and Wales,” said England coach Steve McNamara.
“He has trained hard during our camp and has been an integral member of the squad. The lad is devastated to miss out. He was looking forward to the month ahead with England and making a huge impact.
“The important thing now is for him to rest, rehabilitate and get himself ready for the new season. He has a big 12 months ahead and can be part of our World Cup aspirations.”
However McNamara is unlikely to call a replacement into the squad and so looks likely to play captain Kevin Sinfield in the halves alongside Rhinos team-mate Rob Burrow.
“I will stick with the current group of players and will probably not add to the squad,” he added.
“I do have the option, if I desire, to bring in an extra player but at this stage I don’t envisage adding to the 23 now that Rangi is out.”