The Everton midfielder has been out of action since suffering the horrific injury in the Merseyside club's 4-0 FA Cup win at Stevenage late last month.
Oviedo, 24 required major surgery after fracturing his tibia and fibula bones, seemingly ending his hopes of competing in the World Cup for Costa Rica.
However, Martinez has revealed that the former Copenhagen man has made surprising progress in his rehabilitation and could yet feature for his country in Brazil.
"I've never seen anything like it before," Martinez said. "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.
"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.
"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."
Ella Toone: Why isn't the midfielder playing for Manchester United and England?
'David Beckham was desperate to play in my squad, but I didn't want to bring him along and waste the FA’s money: I had to pick the strongest players': Great Britain coach reflects on Becks snub as 'one of the toughest decisions' of his career
