Anderson, England's all-time leading Test wicket-taker, left the field three balls into his ninth over in Australia's second innings on the second day at Edgbaston on Thursday -- his 33rd birthday.
An England and Wales Cricket Board statement issued Friday confirmed that, following an overnight assessment, he had suffered a side strain.
"England bowler James Anderson has been ruled out of remainder of the current Investec Ashes Test with a side strain," the statement said.
Anderson, whose 413 Test wickets are an England record, took an Ashes-best six for 47 as Australia were skittled out for just 136 in the first innings at Edgbaston.
Recalled fast bowler Steven Finn then took five for 45 on Thursday as Australia slumped to 168 for seven in their second innings, a lead of just 23 runs with three wickets standing.
When he saw Anderson struggle before going off the field after pulling out of his action on Thursday, England great Ian Botham said he feared the Lancastrian would miss the rest of the series.
"If it's an intercostal, we won't see him again in this series," former pace bowling all-rounder Botham said on Sky Sports.
"You can't sneeze, can't cough, can't laugh. You have to let it heal."
Meanwhile six of his 18 returns of five wickets or more in Test innings have come at the Nottingham ground.
He also took 10 wickets across the match in the last Ashes Test at Trent Bridge, in 2013 -- one of two 10-wicket returns he has at Nottinghamshire's headquarters.
England could now recall Durham fast bowler Mark Wood, who took part in the first two Ashes Tests but was ruled out with ankle trouble and replaced by Finn at Edgbaston, into their squad for the fourth Test.
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