The Everton man will undergo surgery on Monday following the serious injury he sustained during Saturday's 4-0 FA Cup fourth-round win at Stevenage.
Oviedo is facing a lengthy spell on the sidelines, but Everton boss Martinez is backing the full-back to make a swift recovery and believes the 23-year-old Costa Rica international could still feature in the Brazil showpiece - which starts in June.
The Spaniard said: "He's in great spirits, it has been two difficult days but he has been inundated with messages from Everton fans.
"He is incredible, he's a really positive guy and leaving the field (at Stevenage) he was telling the players to win the game, but when he got in dressing room the reality kicked in.
"Today is an important day because he's going to have surgery. From then on he's going to be counting down the days until he gets fit.
"It's one of those situations that they could give you a very broad timescale (for how long Oviedo will be sidelined). They always say these things take between five to six months, but it depends on how the surgery goes.
"I think (with) Bryan it'll be a lot less than that. We want to help him get back in time for World Cup.
"I don't think anyone can say he's going to miss the World Cup because it's still up in the air."
Martinez revealed that Phil Jagielka and Sylvain Distin will be assessed ahead of Tuesday's Merseyside derby against Liverpool at Anfield as the influential defenders are carrying knocks.
Steven Pienaar (groin), Antolin Alcaraz (muscle fatigue) and Ross Barkley (broken toe) are rated as doubtful, while Gerard Deulofeu (hamstring) is set to return against Aston Villa on Saturday.
Martinez expects to find out in the next 48 hours if John Heitinga will stay at Goodison Park amid interest from a club in Italy and a Turkish side, believed to be Galatasaray.
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