Lesh posted a message on Saturday (17Oct15) on the Facebook.com page for his restaurant Terrapin Crossroads, editors at Billboard.com report.
He is currently undergoing treatment at the Mayo Clinic in Scottsdale, Arizona, and has had surgery to remove the tumours. He wrote that he is expected to resume "normal activities" after his treatment for the non-aggressive cancer.
The musician also battled prostate cancer in 2006, and made a full recovery.
Lesh's gigs with his band Phil & Friends at the Terrapin Crossroads in San Rafael, California on 24 and 25 October (15) have been cancelled and will be rescheduled.
Consoling his fans, Lesh even offered to pop into his restaurant and "jam in the bar" before he continues with the band's tour dates in New York at the end of October and the beginning of November (15).
He wrote, "I was diagnosed with bladder cancer in early October, and have spent the last few weeks at the Mayo Clinic in Scottsdale doing tests and eventually surgery to remove the tumours. I am very fortunate to have the pathology reports show that the tumors are all non aggressive, and that there is no indication that they have spread.
"So thanks to my local doctor Cliff Sewell, and the incredible team at the Mayo Clinic, all is well and I can return to normal activities in two weeks from my surgery. Unfortunately, that means I will have to cancel the PLF shows scheduled for Oct 24/25.
"We will reschedule these shows as soon as we can, but in the meantime, keep a lookout for a free Grate Room show before I leave for the East Coast shows. I also plan to pop in and jam in the bar before we leave, so I hope to see you there at Terrapin."
Lesh was part of the Grateful Dead's Fare Thee Well concerts in Chicago, Illinois to celebrate their 50th anniversary earlier this year (15), with President Barack Obama describing them as "an iconic American band".
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