Anderson bowled just four overs in the first innings before leaving the field, but managed a tentative jog on the second morning, and will bat if required.
The seam bowler had a scan on the first afternoon, but the results have thus far been kept private. Anderson has missed the last month with an injury to the same calf.
“He is down, he’s frustrated… he actually came and said sorry to all the bowlers, not that he’s got anything to be sorry for,” said Stuart Broad, who took five wickets in Anderson’s absence.
One bowler who will not figure in the Ashes is Mark Wood.
The fast bowler suffered a side strain during England’s World Cup Final triumph and after further assessment the injury has been deemed serious enough to rule Wood out of the rest of the summer.
Wood will also have surgery on his knee to fix some cartilage damage and will plot a return for England’s winter tours.
England have released Sam Curran, Olly Stone and Jofra Archer back to their counties to play T20 cricket in the Vitality Blast, while Archer will also turn out for Sussex’s Second Eleven in a bid to prove his fitness and form with the red ball.
Archer, who has also been suffering with a side strain, would likely replace Anderson should the Lancashire bowler be unable to figure in the second test, which starts at Lord’s on August 14.