The on-loan midfielder is currently building up his fitness at parent club Barcelona after suffering the problem on December 14.
Deulofeu is expected to be back at Goodison Park by the start of February.
"Gerard is progressing really well," Martinez is quoted as saying by Sky Sports News. "We are happy with his progress and he is doing really well and I don't think it will be long before he is back. We reassess him every three days. Hopefully he will carry on with no setbacks."
Everton return action on Saturday when they travel to Stevenage in the fourth round of the FA Cup.