Wood, whose career has been blighted by fitness issues, suffered the injury during Friday's third day of England's five-wicket win over Sri Lanka in the first Test at Old Trafford.
The 34-year-old express quick left the field just two balls into his 11th over.
He didn't feature on Saturday as England went 1-0 up in the three-match series by winning with more than a day to spare, although there were times, on a slow pitch, when they missed the point of difference provided by Wood's speed.
Leicestershire's 20-year-old left-arm paceman Josh Hull has received his first senior call-up to replace Wood in the squad for the remaining two Tests at Lord's, starting on Thursday, and at The Oval commencing September 6.
The 6ft 7in (2 m) Hull has been a key figure in Leicestershire's bowling attack of recent seasons and starred in their 2023 One-Day Cup final triumph.
England already have another fast bowler in their squad in Olly Stone, who could now be in line to play his first Test in three years.
Hull only turned 20 earlier this week and has played just nine first-class matches, taking 15 wickets at an expensive average of 58.06.
Under coach Brendon McCullum, the current England regime have shown a willingness to select on potential and skill-set rather than figures.
Earlier this month, Hull made his debut for the second-string England Lions, taking 5-74 in a seven-wicket win over Sri Lanka.
'Special moment'
But he was not expecting a call-up to the senior squad, with the towering Hull telling BBC Radio Leicester: "It was about half nine (2030 GMT) last (Saturday) night when I got the call from Brendon McCullum. It's a very special moment.
"It's come around pretty quickly, I didn't think it would happen this fast, but I am really excited to be joining them.
"I was happy with how I performed (for the England Lions) but I never thought it would lead to a call this early.
"They've got Olly Stone there as the first replacement, so it will be a great opportunity to join up and be part of that environment."
England are rejuvenating their pace attack following the retirements of veterans Stuart Broad and James Anderson, with Gus Atkinson making an exciting start to his Test career.
England have had to alter the balance of their side after regular captain Ben Stokes was ruled out of the Sri Lanka series by a torn hamstring, with Ollie Pope appointed as stand-in skipper.
