Rodriguez had batted twice in the game against Detroit starter Max Scherzer, striking out in the second inning and flying out to short right in the fourth. On neither at-bat did he appear to have hurt himself.
Also, New York right fielder Nick Swisher came out in the sixth inning with tightness in his right forearm.
Yankees manager Joe Girardi, asked after the game whether he expected to have to field a team minus three of his most potent bats on Tuesday (Lance Berkman also was out of the lineup due to an ankle injury), answered tersely, "Hypothetically, yes.''
Asked how that would hamper his ability to manage the ballgame, he said. "Well, it would leave us a little short, that's for sure.''
Beyond that, the manager didn't have much to say about an injury bug that is suddenly taking huge bites out of his aging roster.
Rodriguez, who apparently injured himself on a swing in the fourth inning, left the clubhouse before reporters were admitted, but Girardi said, "Would I be a little bit surprised if he [Rodriguez] played tomorrow? Yes. But not completely. Whenever a guy comes out, you don't expect him to play the next day. But maybe he'll be available to us as a DH. I'm just not sure yet.''
He offered no prognosis on Swisher other than to say the injury, which he described as "a tennis-elbow-type thing," was not related to the biceps tendon injury that sidelined him for a few games in May.
"I been feeling it for awhile, but this week, it just didn't go away,'' said Swisher, who left for pinch-hitter Marcus Thames after striking out his first two times up. "I just want to get the pain out of there.''
Asked whether he expected to play Tuesday, he said, "I'd like to think so. I want to be out there with my teammates, my guys, fighting with them. But it's not my decision.''
The only one who is sure not to play is Berkman, who hurt himself stepping on the foot of pitcher Bryan Bullington while running out a double play in Sunday's 1-0 loss.
"Unless I have some kind of miraculous recovery overnight, I'm probably not playing,'' said Berkman, whose ankle was swollen and heavily taped as he left the ballpark. "I woke up this morning, and it was a lot worse than I thought it was going to be.''
Berkman said the three-hour flight from Kansas City did not help the injury, which swelled badly on the plane. "It's not good,'' he said.
Right now, the Yankees are looking at a Tuesday lineup featuring Pena at third, Thames or Jorge Posada at DH and Austin Kearns in RF. "We're banged up, but so is everybody this time of year,'' Girardi said. "We'll just have to make do with what we have.''
Information from ESPNNewYork.com's Wallace Matthews and The Associated Press was used in this report.