Kompany was sidelined for two months at a crucial stage of the Barclays Premier League campaign after suffering a calf injury in an FA Cup tie at Stoke in January.
The 27-year-old's return took longer than expected and eventually sparked a club-versus-country row between former manager Roberto Mancini and Belgium.
Kompany has also been troubled by similar problems in the past but Kidd played down concerns after the defender played the first half of City's first post-season friendly against Chelsea in St Louis.
Kidd said: "After the FA Cup final he was feeling his calf and he didn't do any training.
"In the Reading game, we were desperate to get a point to finish second - it would have been a travesty if the lads hadn't done that, so that was paramount - but Vinny had the problem with the calf and couldn't make it.
"Vinny was obviously wanting to play the last game of the season but for one game it wasn't worth the risk.
"It's great to have your captain back and here was fantastic but coming up to the Norwich game he had one day on Saturday and it wasn't worth taking the chance."