"I greatly appreciate the outpouring of support," the Republican senator wrote on Twitter. "Unfortunately for my sparring partners in Congress, I'll be back soon, so stand-by!"
"Subsequent tissue pathology revealed that a primary brain tumor known as a glioblastoma was associated with the blood clot," the hospital said in a statement.
According to the hospital, McCain and his family are reviewing further treatment options, which may include a combination of chemotherapy and radiation.
His Senate office said he is in "good spirits" and recovering at home in Arizona with his family.
"Further consultations with Sen. McCain's Mayo Clinic care team will indicate when he will return to the United States Senate," the statement said.
When the news came of his diagnosis, Democrats and Republicans offered well wishes to him and his family.
Asked about McCain, one of his closest friends in the Senate, South Carolina Sen. Lindsey Graham, said, "He has called me three times this morning. 'No more woe is me, Lindsey.' He is yelling at me to buck up. So I'm going to buck up."
Graham said that he believed doctors removed almost all of the tumor.
"The disease — I think they got it. He's going go through radiation and chemo. I'm not a doctor. It may come back again, and he'll fight it again. But right now, he's in good spirits. It was a really tough operation," Graham said.
"But John is ready to come back," he continued. "And going forward, he's excited, quite frankly, about getting a chance to finish things that have been stuck."
Graham added that without McCain on Capitol Hill, "It's quieter. It's hugely different because John is a fighter and he jumps into every cause, no matter how hard it might be. The energy he provides — he's coming back."