The Nottighamshire left-arm quick missed England's 79-run win at Lord's on Sunday in the first of a three-match series with a viral infection.
But he took part in England's practice session at Edgbaston on Tuesday.
Sidebottom was replaced at Lord's by Liam Plunkett, who took two wickets for 38 runs in 10 overs after being omitted from the two-match, drawn, Twenty20 contest.
Paul Collingwood, England's new one-day captain, said Sidebottom's return to fitness had left him and coach Peter Moores with a selection problem.
"Sidebottom would have been playing at Lord's," Collingwood said here Wednesday. "We will have to assess what our next team is going to be.
"But that's the great thing at the moment, that there is a lot of competition at the moment for certain places, and that's tremendous for the England team," added Collingwood as he reflected on the rest of the England seam attack.
"Stuart Broad (three for 20) was exceptional. Jimmy Anderson (two for 23) started off really well and Liam Plunkett also did well. There is not a lot of experience with Plunkett and Broad but they were magnificent."
The one-day series against the West Indies ends at Trent Bridge on Saturday.