Roberto Martinez described it as "good news" because the club had feared more serious damage to the player's medial ligaments after what the Everton manager called a "stupid challenge" by Alex Oxlade-Chamberlain in the Premier League on Saturday.
"After the game we expected the worst," Martinez told a news conference ahead of Tuesday's Capital One Cup fourth-round tie at home to Norwich City.
"It's probably the least (bad) it could be. I wouldn't expect anything longer than eight to nine weeks and we've got an international break in the middle so hopefully he's not going to miss too much action."
Jagielka will be out of contention for England's friendlies against Spain and France next month.
After beating lower division opposition in the previous two Capital One Cup rounds, Martinez is targeting a place in the last eight of a competition Everton have never won.
"Any success is important to reach what we want to achieve," he said.
"We have a long-term ambition to become a winning team. The only thing that matters now is to get in the quarter-finals of this competition."
(Reporting by Steve Tongue; Editing by Tony Jimenez)
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