The singer, 57, is to undergo surgery, and is expected to make a full recovery but will require a "lengthy" rehabilitation period, the statement said.
"Over the last few weeks I haven't felt good and I didn't know what was going on," Jones said in a statement. "We just found out that I have a stage-one tumor on my bile duct. Luckily we caught it really early and fast and the doctors say it's operable and curable!"
Bile ducts carry bile produced by the liver from the gallbladder into the small intestine to aid with digestion.
Sharon Jones & the Dap-Kings are best known for the 2007 song "100 Days, 100 Nights" and 2010's "I Learned the Hard Way."
The group's fifth album, "Give the People What They Want," was scheduled to be released on August 6. A new release date has not been announced.
The band is credited with reviving interest in soul music over the past decade and preceding such acts as the late British soul singer Amy Winehouse.
Without Jones, the brassy Dap-Kings have also provided backing music to such artists as Winehouse and British rockers The Heavy and Muse.
(Reporting by Eric Kelsey; Editing by Piya Sinha-Roy and Mohammad Zargham)
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