The 20-year-old left training with his leg in a brace earlier this week after suffering medial ligament damage.
Barkley was expected to miss the next six weeks, but Martinez is fearing the worst, saying that he could be out for "anything from seven weeks to four or five months".
"With the swelling we don't really know how bad the injury is," BBC Sport quotes him as saying. "He had a scan but it was a bit difficult to determine the extent."
Everton kicked off their Premier League season with a 2-2 draw against Leicester City earlier today.