The intestinal infection stems from diverticulitis, a digestive disorder, and not brain cancer, the statement said.
McCain revealed last year he's fighting a fatal form of brain cancer called primary glioblastoma and has undergone treatment for the illness.
"Over the last few months, Senator McCain has been participating in physical therapy at his home in Cornville, Arizona, as he recovers from the side effects of cancer treatment," according to the statement.
His daughter, Meghan McCain, confirmed in a tweet Monday that her father is in stable condition.
He “continues to inspire me everyday with his intense grit and determination,” she wrote.
>> Related: Read Meghan McCain's statement about her father's brain cancer
McCain "has remained engaged on his work as chairman of the Senate Armed Services Committee, and has enjoyed frequent visits from his family, friends, staff and Senate colleagues," according to the statement.
McCain’s brain tumor was discovered during a routine screening for skin cancer. He was also diagnosed with melanoma in 1993, 2000 and 2002, and underwent treatment at the time. Those cancers did not spread, according to McCain’s doctors.
>> Related: Photos: Sen. John McCain through the years
Glioblastoma, though, is a particularly aggressive form of cancer, according to the American Brain Tumor Association. The prognosis is often poor. The average survival rate for patients with malignant glioblastoma tends to be around 14 months with treatment. Around 10 percent of patients with the disease live five years or longer.
Debbie Lord contributed to this story.