The 30-year-old was informed that he had liposarcoma - a rare form of cancer that affects fat cells - earlier this year and is now in remission.
In a statement, Revolution said: "It was important for Charlie to concentrate on his family and treatment during the past few weeks and the club honoured his wish for privacy.
"The New England Revolution will continue to support him through full recovery and are looking forward to seeing him back out on the pitch."
Davies last turned out for the Revolution on April 27, when he came off with a groin strain. He is thought to have been back in training for the last fortnight but has yet to feature for his side, who are currently sixth in the Eastern Conference.