England's record wicket-taker broke down after just four overs in the series opener at Edgbaston and did not bowl again as Australia romped to a 251-run victory.
Scans have confirmed he has no chance of taking part in next week's game at Lord's, with assessment taking place "on an ongoing basis" regarding his comeback.
Anderson, 37, was not expected to be on duty in the second Test after his bit-part role in Birmingham. The veteran had not played competitive cricket for a month leading into the match after injuring the same calf on duty for Lancashire and was restricted to two batting cameos at No 11 after pulling up on the first morning.
An England and Wales Cricket Board revealed an MRI scan had settled the matter.
"The MRI confirmed that Anderson has suffered a calf injury," read a statement.
"As a result of the injury, he will commence a rehabilitation programme working with the England and Lancashire medical teams.
"Anderson will miss the second Test match, which starts at Lord's on Wednesday August 14. He will be reassessed on an ongoing basis regarding his availability for the rest of Specsavers Ashes series."
Former England captain Michael Vaughan does not expect to see Anderson on duty again until the fourth Test at the earliest and warned his absence could have a big impact in both dressing rooms.
"I can't see him playing too much of a role in this series," he said on BBC 5 Live's Tuffers and Vaughan Show.
"I can't see how they'll allow him to come back without playing at least a a couple of games first. You're looking at, if everything goes rosey, Old Trafford, but that would probably be a risk.
"My concern is you don't underestimate the psychological effect of Jimmy Anderson has on the England team, but also the positive effect it sends through the Australia team.
"For them to arrive next week and the week after to know they won't be facing Jimmy...that is monstrous."
A debut for Jofra Archer, one of the stars of England's World Cup-winning campaign, could lessen the blow but he must first prove his own fitness for the rigours of Test cricket.
He was carrying a side strain throughout the tournament and has been sent to play for Sussex 2nd XI over the next three days to get long spells with the red ball under his belt.
England captain Joe Root denied England has gambled on Anderson's fitness in the first place and is confident Archer will not represent a gamble if he gets through the required workload this week.
"Jimmy passed every medical testing. He was fit to play. It's one of those freak scenarios where he pulled up," said Root.
"It's an easy thing to look back on and say we'd have done things differently. It was a unanimous decision for him to play.
"With Jofra, we're in a slightly different situation where he'll have played a lot of cricket in between and we'll have a clearer idea of where he's at. We'll turn up to Lord's and make sure in the next few days we don't make any shotgun decisions."