Kubiak was taken to a local hospital in an ambulance with his family and was conscious, according to the Texans. The team said Kubiak did not have a heart attack and was in stable condition.
"He had an episode, he was light-headed and dizzy," Houston general manager Rick Smith told NBC during a postgame interview. "He was evaluated by a number of specialists ... he is awake and coherent.
"… Hopefully, Gary will be back with us tomorrow."
Kubiak remained hospitalized Monday morning and doctors were conducting more tests to determine what caused him to collapse, a source told ESPN NFL Insider Adam Schefter. They still have not made a final determination. They believe dehydration could be a part of it, but they also are testing for more significant reasons, the source said.
The 52-year-old Kubiak fell to his knees and grimaced when he collapsed, but he never lost consciousness.
"It was really weird," Texans quarterback Case Keenum said. "Someone came in [to the locker room] and started yelling for a trainer. They said that he had passed out and we were all very worried."
The coach was conscious, alert and "feeling good" Monday, the source told Schefter.
Kubiak lay on the ground for several minutes and was surrounded by medical personnel, including Texans head trainer Geoff Kaplan. After a few minutes, Kubiak sat up and spoke with those surrounding him before eventually being strapped to a stretcher and taken off the field.
Defensive coordinator Wade Phillips took over in the interim.
"There was a lot of unknown," Phillips said. "Everything was unknown as to what was going on and what happened to Kub. [Offensive coordinator] Rick Dennison obviously called the plays from the press box. We had to adjust as far as the head coach not being there. But it was a shock to everybody."
Houston led the Colts 21-3 at halftime but wound up losing the game, 27-24.
Kubiak has been the Texans' coach since the 2006 season.
His collapse came a day after Denver Broncos coach John Fox was hospitalized in North Carolina after feeling light-headed while playing golf. Fox is expected to have aortic valve replacement surgery this week and is expected to miss several weeks.
Information from The Associated Press was used in this report.