Crosby will not play in Monday's game against the Lightning, but "specialists believe he should be through the infectious period by Monday."
The Penguins announced on Friday that Crosby would miss Pittsburgh's next two games with an illness, and would sit as a precautionary measure.
Crosby's face was visibly swollen when he spoke to the media on Friday.
Crosby is the lastest in a string of NHL players to be diagnosed with the mumps this season. The illness is a viral infection that causes swelling in the salivary glands.
Last month, Anaheim Ducks players Corey Perry and Francois Beauchemin both were diagnosed with the mumps, followed by Wild defensemen Jonas Brodin and Marco Scandella. Wild defenseman Ryan Suter was diagnosed with it earlier in December.
Crosby, who won the Hart Memorial Trophy last season, has nine goals and 26 assists in 27 games in 2014-15.
- Molly Geary