Pagano, who turns 52 this week and is in his first season with the Colts, was diagnosed with the illness during the team's bye week after leading them to a 1-2 start.
He will be hospitalised for six to eight weeks to receive treatment during which time his offensive co-ordinator Bruce Arians will take charge.
"I am optimistic. I feel with every fibre in my body and I know Chuck feels the same way, that he can beat this thing," said Indianapolis owner Jim Irsay.
"It's unlikely that he will be all-in as a head coach this season, that's probably not in the cards. ... Certainly to be in the press box, to contribute, to do things, I'm going to let the doctor be more specific about that with his expertise on how this process goes but there are peaks and valleys."
The Colts' next game is at home to the Green Bay Packers on October 7.