The decision comes after bassist Ted Dwane received treatment this week for a blood clot on his brain.
The band made the announcement on its Facebook page.
The band postponed three shows earlier this week after the blood clot was discovered, but hoped to play Bonnaroo on Saturday night.
There is no word on what act will replace Mumford & Sons in the headlining slot in front of 80,000 fans.
Dwane is recovering from the procedure and was not ready to play Saturday.
Rather than perform with a replacement, the London-based Grammy-award-winning folk rock band decided to pull out.