The 23-year-old was hurt in a heavy challenge during the first half of the 2-0 international friendly win over Poland in Dublin on Wednesday.
He managed to play on after receiving treatment with the full extent of the injury only becoming clear after the game.
Sunderland manager Martin O'Neill said: "We have a problem with James McClean, who picked up an injury during the course of the (Wednesday's) game.
"He hurt himself in the first half, but continued in the second half and came off after, I think, 80 minutes in the match and arrived here, where his ankle is particularly swollen. That's causing us some concern at the moment."
McClean has made 31 appearances for the Black Cats this season, scoring five goals.
Striker Danny Graham - signed from Swansea on deadline day - is expected to make his home debut for Martin O'Neill's side against the Gunners on Saturday.