Iwobi was carried off on a stretcher early in the second half as Everton lost 3-1 to United in Friday's third-round match.
"Scan results on Saturday confirmed a lateral ligament injury that will be managed conservatively by the club's medical team at Finch Farm," Everton said in a statement.
Everton are 18th in the Premier League table on 15 points and host bottom side Southampton on Saturday.