"He will not play a rehab game before he has the MRI," Girardi told reporters, according to the New York Post.
Rodriguez, who has a strained right quadriceps, ran in the outfield before New York's game against the Cleveland Indians on Wednesday night. He also played catch, fielded grounders and took batting practice.
"There's nothing that's happened, but they want to make sure on the MRI that it's healed enough for him to take the next step," Girardi told reporters, according to the New York Daily News. "It's always a little bit different when the intensity has to be turned up, when you have to make the quick break and everything isn't calculated. But it is a good sign what he did today."
Rodriguez, a three-time AL MVP, is expected to continue with a similar routine over the next few days before possibly playing in extended spring games Monday and Tuesday in Tampa.
"He said it feels great right now," Girardi said before Rodriguez did his pregame drills. "But it's a different beast when you have to run so we're going to have to see how it feels when he runs."
The Yankees begin a four-game series at Tampa Bay on Monday and Rodriguez is eligible to come off the DL next Wednesday.
Rodriguez told reporters that his DL stint might have been a blessing in disguise.
"Being on the DL is probably the best thing that could have happened to me," Rodriguez told reporters. "Knowing me and knowing my history, I probably would have been out there doing something stupid to screw up the whole season. The DL is a good shelter."
Still, Rodriguez is optimistic he will return next week.
"I'm really optimistic," he told reporters, according to the Star-Ledger of Newark, N.J.. "It's something where until you actually sprint in a game and let it go 100 percent, you're really not going to know. Right now, it's just building strength and getting it right."
Information from The Associated Press was used in this report.