The first-year coach, who turns 52 on Tuesday, was diagnosed with acute promyelocytic leukemia and will be "lost to the club for a period of time," the Colts reported on their website.
Pagano was diagnosed with the illness last week when the Colts were on a bye week and he is already in hospital receiving treatment.
"It's been a very difficult week," team owner Irsay said in comments reported by the Indianapolis Star. "I am optimistic. I feel with every fiber of my body and I know Chuck feels the same way that he can beat this thing.
"He's upbeat and he's ready for the fight. He's tough as nails. He's in great spirits."
The paper also quoted Irsay as saying it is unlikely that Pagano will be able to fully resume his job this season.
Offensive coordinator Bruce Arians has been named interim head coach of a Colts team that will host the Green Bay Packers on October 7.
Pagano, who was previously defensive coordinator of the Baltimore Ravens, took over the Colts head coaching job this season and his team is currently 1-2 in the AFC South.