Doctors in France, where Faithfull was diagnosed, say the cancer is in its earliest stages, said publicist Rob Partridge.
Faithfull, 59, had been due to begin a world tour next month, but it has been postponed until next year.
"I have absolute faith and confidence in my fantastic medical team and of course I will be well again, if not better than ever," the British singer-actress said in a statement released by Partridge.
"Next year's tour, I want to assure fans, will be one big celebration."
Partridge said the cancer had been "quickly discovered by doctors in France — where Marianne stays when not at home in Ireland — and the prognosis for a return to full health is excellent.
"Indeed, Marianne Faithfull is looking forward to playing the rescheduled tour in 2007," he said.
The tour had been due to kick off in Paris on Oct. 7, with concerts in the United States, Canada, Holland, Sweden, Norway, Switzerland, Hungary and Spain before ending in London on Dec. 18.
Faithfull gained fame in the 1960s as the girlfriend of Mick Jagger and as the pure-voiced singer of "As Tears Go By." After battling drug addiction, she re-emerged in 1979 with the raw album "Broken English" and has since found a new audience as a sophisticated chanteuse.