The 20-year-old was injured in training and played no part in Saturday's 2-2 draw at promoted Leicester City on the opening day of the Premier League season.
Martinez said he was hoping for the best, but feared that the midfielder may miss a significant part of Everton's season and several of England's Euro 2016 qualifiers.
"We had a scan, but it was difficult to determine the extent of the injury. It is a problem with a medial ligament in his knee, but we don't know how bad the injury is," he said.
"We know there is a partial tear of the ligament and that could mean anything from seven weeks to four or five months, so we need to be cautious."
Everton could have used Barkley's power and flair as they failed to defeat Leicester despite leading twice through goals by Aiden McGeady and Steven Naismith after City's record signing Argentine Leonardo Ulloa had put the home side in front.
Chris Wood struck an equaliser late on for Leicester.
"I think Ross Barkley is a phenomenal footballer and we are going to miss him – there are no two ways about it," Martinez said. "He was so sharp in pre-season and I think he came back with a different approach and a different mindset.
"The squad should be big enough and be able to cope with losing a player, but it is disappointing."
Adding to Martinez's unease was the two points his side threw away at Leicester.
"If I have a criticism from our point of view, it's that maybe we should have gone for that third goal with a little bit more brightness rather than just controlling the game," said Martinez, who led Everton to fifth last season.
(Reporting by Martyn Herman; Editing by Ken Ferris)
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