The Republic of Ireland international was stretchered off during the 3-1 World Cup qualifying win over Kazakhstan on Tuesday night having made his return from international exile in the 3-0 defeat by Germany last Friday.
Scans on Wednesday confirmed the 25-year-old will need surgery, but Martinez remains optimistic.
"Yesterday's scans showed that his ACL is ruptured, but the knee reacted well and nothing else is damaged," he said.
"We look forward to seeing Darron back, hopefully this season. Taking into consideration what it could have been, it was positive news."
Everton host Hull City on Saturday looking to bounce back from their first defeat of the season at Manchester City before the international break.
"I think Hull City have had a very good start to the season. No one talks about them as a newly-promoted side anymore," added Martinez, who is looking forward to having Steven Pienaar available for selection soon.
"Pienaar's been working well with the group. This weekend could be too early but I expect him to be fully fit for next Saturday."
Antolin Alcaraz, signed on a free from Wigan in the summer, is yet to feature this season and is a little further away from featuring.
"Alcaraz is looking very strong. He has fully recovered after a setback three weeks ago. We expect him to be involved within three weeks."
Martinez was full of praise for his left-back Leighton Baines following his performances for England in their final two World Cup qualifiers.
"It was an outstanding contribution," he added. "I thought the game against Poland he was really, really influential, he enjoyed his football, he showed just where he is at his career.
"From our point of view Leighton Baines' performance is something that we see week in week out. It's great to see that when you have a player on international duty, it shows you the maturity and how ready he is to perform in that manner."
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