Ted Dwane had an operation for a blood clot on the surface of his brain this week.
He is now "on the road to a full recovery," the band said in a statement on its Facebook page Thursday, but he needs time to recover from his health crisis.
The band, which was supposed to perform at Bonnaroo Saturday, also canceled a gig at Colorado's Telluride Bluegrass Festival next week.
"If we could've we would've, you know that about us," the musicians said in their Facebook message. "We trust that you can respect our collective desire to encourage Ted to make a full recovery, and that this is based purely on the medical advice we have received."
Billboard.com said no replacement for Mumford has been announced yet.
2014: The Year in Music [PHOTOS]