The Nottinghamshire left-arm quick did not join the England one-day international squad in Southampton on Sunday and will continue to receive treatment at the National Cricket Performance Centre, the ECB said Monday.
The 29-year-old has undergone rehabilitation treatment there since suffering the injury during the drawn third Test with India at The Oval, which concluded on August 13. India won the series 1-0.
A further assessment will be made following Tuesday's first one-day international at the Rose Bowl to determine when Sidebottom will be available to join the England squad.
A replacement has not been called up at this stage but further consideration will be made following Sidebottom's fitness assessment after the opening India match.
The second game of the seven-match series takes place in Bristol on Friday.