The Lancashire quick's place in the 15-man party has been taken by Worcestershire seamer Kabir Ali, who has already played 12 One-day internationals, although England are hopeful that Chapple could still feature at some stage during the five-match series.
Chapple, a long-serving county performer, only made his England debut in Tuesday's inaugural One-day international against Ireland in Belfast.
But the 32-year-old managed just four overs before leaving the field injured.
Chapple underwent a fitness test earlier Thursday but it was found he had not recovered sufficiently to play in England's Twenty20 match later in the day against Sri Lanka and the opening fixtures of the One-day series.
England chairman of selectors, David Graveney, said: "Obviously it's very disappointing for Glen but everyone hopes that after receiving the right treatment at Lancashire he'll be able to rejoin the squad and play a part in the latter stages of the NatWest Series."
The series begins at Lord's on Saturday with further matches on June 20 at The Oval, June 24 at Riverside, June 28 at Old Trafford before concluding on July 1 at Headingley.