He will be replaced on an interim basis by offensive coordinator Bruce Arians.
Team owner Jim Irsay made the announcement Monday during a somber and sometimes emotional news conference at the team complex.
"I think it's unlikely he'll be all in as the head coach the rest of this season," Irsay said. "He may be able to come back and be in the press box or something."
The 51-year-old Pagano is in his first season with the Colts (1-2). He was hired in January after serving as the Baltimore Ravens' defensive coordinator.
Dr. Larry Cripe, the physician treating the coach at Indiana University's Simon Cancer Center, said Pagano has acute myeloid leukemia, where the bone marrow is producing abnormal white blood cells that interfere with healthy blood cells. Symptoms can include weakness, weight loss and easy bruising or bleeding. Treatments can include chemotherapy, drugs and radiation therapy.
Irsay said Pagano's wife pushed him to see the doctor after noticing unusual bruising on the coach's body.
The initial phase of treatment usually requires a hospital stay of four to five weeks, though Irsay later acknowledged he expected Pagano to be in the hospital at least six weeks.
Cripe said Pagano began the "arduous" treatment last week and that many adults do recover from the disease. For now, Pagano is being kept in a "protected" hospital environment where air is filtered and hand-washing is essential.
Pagano was admitted last Wednesday evening; the team had a bye this weekend and players and the assistants, other than Arians, were not told Pagano was ill until Monday morning.
"This is not an easy day for any of us," Arians said. "It was not the way I ever dreamed about addressing a group like this. But I know he'll get through it."
General manager Ryan Grigson said he was not yet certain how the rest of the coaching duties would be split up, though he expected all of the assistants to pitch in.
The Colts are starting over this year after a dismal 2-14 season that led to a major staff and player overhaul. Irsay dumped much of his front-office staff, including Bill and Chris Polian, and let four-time NFL MVP Peyton Manning depart to the Broncos in free agency, giving the reins of the team to No. 1 draft pick Andrew Luck.
The Colts used 15 new starters, including nine on offense, in the season opener at Chicago. Two of the returning starters, Robert Mathis and Dwight Freeney, were playing different positions.
Only 10 players remain from Indy's 2009 AFC championship team and only five were there when the Colts won the Super Bowl after the 2006 season. One of the league's most experienced teams over the past decade started this season as the NFL's ninth-youngest.
When Grigson and Pagano were hired, they wanted to build the new-look Colts around a more balanced offensive approach and a more aggressive defense. Luck has looked solid, rallying the Colts for a Week 2 win against Minnesota, and both the defense and special teams have improved.