The Latics are still reeling from a disastrous night on Tuesday after a 3-2 defeat to Swansea edged them closer to the Premier League trap door.
Martinez has been left counting the cost of the loss ahead of the FA Cup final, with Stam feared to have suffered a broken leg after a heavy challenge during the clash with the Welsh outfit.
The Dutch defender looks certain to miss Saturday's showpiece game with Manchester City and Martinez admits he could face a lengthy spell on the sidelines.
"We will check Ronnie tomorrow, but it seems it is a broken leg," said Martinez.
"He couldn't put any weight on it, so he will need a scan tomorrow to find out exactly what it is."
The Spaniard also revealed the hamstring injury Beausejour suffered at West Brom last Saturday will keep him out of the cup final and his season could also be over.
"It will be difficult for him to be back before the season ends," he added.