Stafford's right knee was twisted on a sack during the fourth quarter of Sunday's loss against the Chicago Bears and he immediately grabbed behind it and screamed in pain on the ground.
"He's day to day and we'll know more on Wednesday," Schwartz said.
Daunte Culpepper replaced Stafford at Chicago and would likely start Sunday at home against the defending champion Steelers (2-2) if the rookie can't play.
But even if Stafford can't practice after Tuesday's off day, Schwartz insisted that wouldn't necessarily rule him out.
"Every situation is a little bit different. Every position is a little bit different," Schwartz said. "Quarterback is probably a little bit different than all of these. He's a young player, he needs more reps, he needs to see things. I wouldn't want to put that set of rules out there beforehand."
Schwartz stuck by one of his policies, limiting information he shares about injuries by declining to say if Stafford's kneecap is dislocated.
"You know my philosophy on injuries as far as commenting on specifics and things like that," he said.
Stafford wasn't in the locker room Monday when it was open for the media, but he told reporters Sunday the same knee was injured in high school.
"He hurt it in a freak accident on a Slip 'N Slide," his father, John Stafford, said Monday night. "After a hot day of working out in the summer with the football team going into his senior year, the guys were messing around on a Slip 'N Slide and he got hurt."
John Stafford said his son sent him a text message Sunday, letting him know he hurt his knee and would have an MRI exam.
"I don't know anything more, but I usually don't get much out of Matthew," he said.
Schwartz did acknowledge tests had been completed on Stafford's knee Monday morning.
"It's just how he responds to it," Schwartz said.
The Lions (1-3) did not respond too well to snapping their 19-game losing streak, losing 48-24 at Chicago.
"A couple of you astutely observed that I seemed a little ticked off after the game," Schwartz said at his weekly news conference. "And I'm here to say that after 24 hours, I'm probably more ticked off now than I was right after the game.
"We never gave ourselves a chance to win that game. There were way too many errors in all phases of the game, but particularly in special teams."
Schwartz announced one change, putting third-round pick Derrick Williams in as a kickoff returner after sixth-round selection Aaron Brown averaged 22 yards on kickoff returns in the four games.
"He was behind in training camp, but our inefficiency in kick returns is glaring and it needs to be addressed," Schwartz said. "He's going to have to do the job for us."
The first-year head coach, though, does not plan to shake up his staff.
"I'm not George Steinbrenner," Schwartz said.
Copyright 2009 by The Associated Press