Mejia felt stiffness in his elbow while warming up Monday and is scheduled for an MRI on Tuesday in New York.
Familia struggled this spring, allowed six runs in nine innings.
However, in Monday's win against the Nationals, Familia hit 97 mph with his fastball and got three, quick outs for a scoreless inning in relief of Bartolo Colon and Carlos Torres.
Nelson Figueroa on WB Mason's Post Game Live: He was successful at throwing his sinker on Monday. It had more movement than I'd seen in a long time, especially during Spring Training. Monday, he was 95 mph, 97 mph, with heavy sink, which at times, they said looked like a split-finger fastball. If you can do that, keep throwing it until the opposition makes an adjustment to it. He looked great today. Now, it'll be interesting to see what role he takes going forward.
Matthew Cerrone, MetsBlog.com: I like Familia as closer, and so do the Mets. The buzz from Citi Field during the last year has been that Familia, not Mejia or even Bobby Parnell, is likely to be the long-term option at closer for this franchise. I see him as a very calm, very focused, very resilient young man, which, to me, is what defines the 'closer's mentality,' not aggression and a fancy celebration. I also like that he doesn't rely only on strike outs. He throws hard and gets swings and misses, but - if entering with runners on base - his slider can get ground balls, which is a helpful tool. The more experience he gets in tight situations, the better, because I think he can have a bright future pitching on the line in ninth innings.