The latest setback is another blow for the left-arm seamer who had already missed the opening three matches, all of which the tourists lost.
After suffering Achilles problems at the start of the tour the 30-year-old complained of discomfort before the third one-day international in Kanpur.
He was sent for a scan and although those results were inconclusive, further tests have revealed a slight tear to his right side.
"We know fast bowlers can pick up niggles," said England coach Peter Moores. "We've had Andrew Flintoff missing for 18 months and he's come back, so we know it happens.
"We also know that people who play international cricket, they have a never-ending schedule because it's a 12-month cycle and they have to get used to that.
"Ryan's given everything for 12-18 months, picked up those niggles and hopefully we can get him fit, strong and his body in the right shape to then carry on playing without injury for a decent period of time."
Sidebottom will now remain with the England Performance Programme squad, who arrived in Bangalore on Saturday.