The 24-year-old left-back required surgery after breaking both the tibia and fibula in his left leg during the FA Cup win over Stevenage last month and the anticipated recovery time put his World Cup dream at serious risk.
Video footage of Oviedo riding an exercise bike was posted on the internet this week, and Martinez, speaking ahead of the trip to Premier League leaders Chelsea on Saturday, said the player had amazed Everton's medical staff with his progress.
"I've never seen anything like it before," he was quoted as saying by the Liverpool Echo on Friday.
"I was talking with the medical staff and we're all staggered. The word is remarkable.
"He's an incredibly quick healer and he's so focused. He's been working non-stop in the little jobs he's got to do daily.
"For him to be able to walk after three weeks and even put weight on the leg, to ride a bike, shows you he's an incredible character.
"He's an outstanding example of how players should be facing adversity. He's never felt down, he's taken each day as one less day until he's back to fitness."
Capped 26 times by his country, Oviedo was given little chance of recovering for the World Cup in Brazil, where Costa Rica will meet Italy, England and Uruguay in Group D.
"I always felt because of the way Bryan is mentally and how focused he is that he had a slim, slim chance of making the World Cup," Martinez said.
"Now I'd be even more positive about it because there's still a long time to go, and if he progresses at the rate he's doing now you could easily see him being fit for mid-June."
Spaniard Martinez said the addition of former striker Duncan Ferguson as a first-team coach was a boost for the club.
"Duncan is developing into a really exciting coach," Martinez said.
"He has been working with the first team on a part-time basis. He has done a really good job with the under-18s and we feel we need his influence around the first team on a permanent basis."
A fans' favourite, Scot Ferguson had a reputation for fireworks on the pitch and returned to the club as a coach under former manager David Moyes.
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