Brazil centre-back Silva missed last Friday's 3-0 win at Bordeaux due to the complaint and has failed to recover in time.
It means 21-year-old defender Presnel Kimpembe is in line to start against Barca's all-star forward line of Lionel Messi, Luis Suarez and Neymar in Tuesday's first leg of a keenly anticipated last-16 tie.
Kimpembe has made 16 appearances for Unai Emery's side in all competitions this season but is yet to feature in the Champions League.
Speaking at his pre-match news conference, with speculation rife over Silva's injury but before his absence was confirmed, Barca boss Luis Enrique acknowledged the 32-year-old's importance to the PSG cause.
"That's something that I just learnt about, that Thiago Silva may not be able to play," he said.
"He is one of the pillars of the team. Personally, I like the best players to play. That will make the show all the better."