Stam had only just been introduced as a second-half substitute when he went down after a heavy tackle.
The Dutchman was unable to return as Wigan slipped dangerously close to relegation, and it is evident he will now miss Saturday's FA Cup final, plus Wigan's final two Premier League games.
"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."
It capped a disastrous night for Wigan, with Martinez also confirming the hamstring strain that kept Jean Beausejour out of this evening's game is also virtually certain to end his season.
"Jean has a tear in his right leg," said Martinez.
"It will be difficult for him to be back before the season ends."