The 23-year-old will have surgery on Monday and is in danger of missing the World Cup.
"Bryan is a really positive guy and has been overwhelmed with the thoughts of every Evertonian," Martinez told a news conference on Monday.
"We'll keep in mind the incredible level he showed this season and we can't wait to get him back. He's been very important for us.
"They say these things take five to six months but I think Bryan may be less. We want to help him get back in time for the World Cup."
Oviedo has been capped 26 times by his country and was almost certain to be named in the squad for the World Cup where Costa Rica will play Italy, England and Uruguay in Group D.
(Reporting by Josh Reich; editing by Tony Jimenez) nL3N0L13GT
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