"He woke up and had a little knee pain," Eppler said. "So, we ended up doing an MRI on both his right ankle and his right knee."
Nimmo was trying to break up a double play at second base on Friday but slid awkwardly into the bag. He stayed down for a few moments before limping off the field with medical personnel.
Eppler termed the sprains "low-grade" and sounded optimistic about Nimmo's road back.
"Everything, structurally, looks sound," Eppler said. "So, he's in a week-to-week situation right now, and we've got some time before Opening Day, so we'll continue to watch him, and we'll probably get an update on him about a week from now."
Nimmo hit .274 with 16 home runs and 64 RBIs last season, helping the Mets return to the postseason.
It's been a tough injury week for the Mets. Closer Edwin Díaz suffered a torn patellar tendon and is expected to miss the entire season after hurting his right knee while celebrating Puerto Rico's victory over the Dominican Republic in the World Baseball Classic.
The Associated Press contributed to this report.