Devine suffered a “really bad” hamstring tear during the Robins’ pre-season defeat by Swansea on 15 July.
The 21-year-old only made two appearances last season because of persistent injuries and was ruled out in March with another hamstring tear.
He returned to the squad over the summer but now faces possible surgery.
“I’m fearing a little bit for Reece because I’m thinking that’s going to need surgery,” head coach Michael Flynn told BBC Radio Wiltshire.
“It’s a very tough time for him, he’s just been through that rehab. When I was at Walsall he was going through that rehab as well and this time now he’s got to do it all again having just come back.
“It’s going to be a real, real test of character but the only thing we can do is be here and support him and do what we can as in duty of care by the football club.”
Clayton, 22, came off after 25 minutes in the same match against the Swans with a groin injury and is waiting for an MRI scan to show the extent of the damage.
He was a regular in the back-line for Swindon last season, playing 34 games for the club in all competitions following his arrival from Liverpool.
“It was very innocuous but it could be anything from six to 12 weeks and I know that’s quite broad,” Flynn said.
“It was a little bit uncertain whether it has actually come away from the bone or not, but if it has come away from the bone I know it sounds worse but it’s actually better because it will actually reduce the rehab time.”
Swindon begin their League Two campaign at Colchester on 5 August.
