Anderson, England's all-time leading wicket-taker, has not bowled in the series since breaking down with the injury after delivering just four overs in Australia's 251-run win in the first Test at Edgbaston.
The 37-year-old Lancashire paceman had tried to get fit for the fourth Test at Old Trafford starting on Wednesday.
But after bowling during a second XI match against Durham this week he has been declared unfit for the final two Tests.
On the same day Australia had better news, with star batsman Steve Smith proving his fitness by batting in his first competitive game since suffering concussion after being felled by fast bowler Jofra Archer in the second Test.
Smith, in the middle for 47 minutes in Australia's three-day match against Derbyshire, faced 38 balls and struck two fours on his way to a total of 23 before he was caught in the deep.
Australia all-rounder Mitchell Marsh, who batted alongside Smith on Thursday, said Anderson's ongoing absence would hurt England.
- 'Devastated' -
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"It's obviously a big loss for them. He (Anderson) has a wealth of experience," Marsh told reporters after stumps.
"I daresay it's probably his last chance to play in an Ashes at home so I'm sure he will be shattered.
"I think England have showed they've got great depth in their bowling attack, so a big miss but plenty to play for still."
"He must be devastated. As a human being, you feel sorry for him. You want to be playing against the best and he's obviously one of the best ever," Marsh added.
"I'm sure the whole of England will be disappointed."
England will travel to Manchester all square at 1-1 in the five-match contest after Ben Stokes's stunning 135 not out saw them to a dramatic one-wicket win in the third Test at Headingley last week.
"Whilst bowling in the ninth over on Thursday in Lancashire's second XI four-day friendly against Durham... Anderson became aware of right calf pain following on from 20 overs he had bowled on Tuesday," said an England and Wales Cricket Board statement issued Friday.
After a medical assessment by Lancashire, Anderson was withdrawn from the remainder of the game with the statement adding that "further review with the ECB medical team has confirmed he will be unavailable for the remaining two Specsavers Ashes Tests".
- Top of the quicks -
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Anderson has taken 575 wickets in 149 Tests at 26.94.
His tally is the most by any seam bowler, with Anderson fourth in the all-time list of leading Test wicket-takers.
And his new-ball partnership with Stuart Broad is the most-successful -- they have taken more than 850 wickets in Tests together.
Anderson may now have made his final Ashes appearance given he will be 39 by the time England tour Australia in 2021/22.
And it's possible his international career could be over, although the prospect of becoming the first fast bowler to 600 Test wickets may spur him on to make a comeback on England's upcoming tours of New Zealand and South Africa.
England have now added Somerset bowler Craig Overton into a 13-man squad for the fourth Test.
Overton and Surrey left-armer Sam Curran, still in the squad after not making the Headingley XI, will likely be vying with Chris Woakes for a place in the side.
Broad has led the way for England with 14 wickets at 25.35 so far this series and World Cup-winner Jofra Archer has added a cutting edge to an attack where Stokes plays a key role.
Despite being dismissed for just 67 in the first innings at Headingley, England have retained the same specialist batsmen, although they could yet rejig their top order.