Oviedo suffered the injury to his left leg during the FA Cup fourth round victory over Stevenage on Saturday, and the Costa Rica international is set for a lengthy absence, which could see him miss the FIFA World Cup in Brazil.
Naismith, who has spent long periods of his career in the treatment room with two cruciate ligament injuries, believes the physiotherapy team at Goodison Park is one of the best in the country and he expects the 23-year-old to make a full recovery.
"All our attentions turn to Bryan," he told the club's official website after scoring twice in the Cup win. "He is a player that in the past three or four months has shown everyone at Everton what he is capable of.
“For something so nasty to happen like that is not very nice at all.
"But I don't think he could be at a better club for his rehab. The physios here are great and we have a squad here that will get behind him and give him the confidence Bryan needs to get himself back."
