Oviedo limped off holding his hamstring after only 25 minutes of the 6-2 win against Sunderland on Sunday and was due to have a scan on Tuesday.
The Costa Rican’s time at Goodison Park has been blighted by injuries, most significantly the double leg break he suffered in January 2014.
Martinez told evertontv: “It is a sad incident because of Bryan’s previous problems.
“He has been fighting to get fit after the horrific break that he had. It seems that when you come back from a long-term injury like that, the whole mechanics of your body suffer a little bit.
“Bryan has been picking up little injuries and niggles but he is such an incredibly driven individual that this will not stop him getting back onto the pitch.
“We are going to find out a bit more about the extent of the injury but we don’t feel it is anything too serious.”