Simon is day-to-day and will continue to receive treatment on the leg during Monday's off-day, with more news expected before Tuesday's series opener against Oakland.
Simon said he felt "a little pop" several steps short of first base, but he was still able to cover the base and record the out on Willie Harris, who hit a grounder to diving first baseman Luke Scott.
Television replays showed Simon coming up short on his stride, and, after securing the out, he grabbed his left leg in pain. Head athletic trainer Richie Bancells and manager Dave Trembley came out to see Simon, and after several minutes, he limped off with the aid of Bancells.
"I just tried to run hard to the base. We'll see how fast I can recover," Simon said. "I think it'll be good in a couple of days, maybe just a week."
Baltimore's de facto closer in the wake of injuries to Michael Gonzalez and Jim Johnson, Simon said he has had hamstring problems in the past. When asked how long it took him to recover from those injuries, he responded "two weeks."
A bullpen without Simon for any stretch of time would be severely limited. The power right-hander had tossed a 1-2-3 ninth to help send the game into extra innings, and after exiting, sidearmer Cla Meredith -- pitching for the fourth time in five games -- surrendered a walk-off homer to Josh Willingham.
"We're a little short-handed down there right now," Meredith said of Baltimore's 'pen, which has also been without the services of Koji Uehara (right elbow strain) since Wednesday.
"Guys are rolling out there, maybe a little tired and stuff," Meredith added. "That's baseball and that's how things are in the big leagues sometimes. Obviously, that's a pretty big blow [if Simon is out]. He's done a great job for us. We'll try to do the best we can."
Simon assumed the closer role out of necessity and has performed better than anyone could have expected. Just over a year removed from Tommy John surgery on his right elbow, Simon entered Sunday 5-for-6 in save opportunities, with a 1-1 record and 3.27 ERA.
With Uehara expected to be placed on the disabled list, manager Dave Trembley said the team will likely add an arm that can go multiple innings. The extent of Simon's injury will also have an impact on the club's roster moves, which could involved adding multiple arms if Simon is unavailable for an extended amount of time.
Brittany Ghiroli is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.