The Arizona Senator's daughter, Meghan McCain, told CNN her father “doing really well” and working on his physical therapy after chemotherapy treatment led to his infection.
Mr McCain was diagnosed with glioblastoma, a type of brain tumour, last July, after having routine surgery to remove a blood clot behind his eye.
Ms McCain said: "He’s doing really good, all things considered. He had sort of a bad bout at Christmas time."
She added: “He had ramifications from his chemotherapy. He had pneumonia. But he’s made this, like, really incredible comeback.”
The Arizona representative returned to his home state, from Washington, before Christmas and this is the first update on his progress for several months.
Ms McCain said the diagnosis had opened her eyes to the struggles millions of individuals and their families have to maintain normal life and work while having “this omnipresent [disease] in everything you do”.
Labour peer and former culture secretary Tessa Jowell, who stood down as an MP in 2015, was also recently diagnosed with glioblastoma.
Last month she opened up about her treatment and called on the NHS to make more medical advances available for cancer patients who have few other options.
She received a standing ovation in the House of Lords after speaking about the issue.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies