Manchester United centre-back Ferdinand, who had been recalled to the squad after a lengthy absence, was poised to feature in the two Group H games but pulled out after speaking to Hodgson on Monday.
The 34-year-old has a detailed pre-planned training and medical programme he has been told to follow to help manage a long-standing back problem.
Hodgson has also lost Tottenham central defender Michael Dawson after he was injured in Sunday's 1-0 defeat to Fulham and has called up Dawson's Spurs team-mate Steven Caulker from the U21 squad as cover.
Manchester City defender Joleon Lescott was also added to the squad on Sunday evening, while Hodgson's other options in the centre of his defence are Gary Cahill and Chris Smalling, with Phil Jagielka another absentee and John Terry now retired from international football.
Meanwhile, Ferdinand has hit back at his critics following his withdrawal.
He tweeted: "I thought these ex sportsman who have experience with injuries + maintenance would know better than to chat rubbish like they are doing."
Ferdinand had been desperate to resume his 81-cap international career, but accepted it was not worth the risk and travelled to London on Sunday to tell Hodgson in person.
"I'm gutted I had to pull out of England squad," Ferdinand said.
"But it was the right decision for my intricate pre-planned programme.
"It was important for me to be able to speak with Roy face to face and explain the situation.
"One thing I made clear was that my passion and commitment to represent my country is as strong as ever.
"It is disappointing that I won't be able to play a part in the upcoming games but I told Roy that I want to continue to be available for England and I look forward to working with him in the future."
Alex Oxlade-Chamberlain has expressed his disappointment at Ferdinand's withdrawal but backed the Manchester United man to play for his country again, while he says the other players in the squad can fill the void.
"He plays for a club like Manchester United so the experience that he can bring to us from his club team and the level he plays at - Champions League football - would be brilliant," said Oxlade-Chamberlain.