The decision came even though former starter Matt Schaub returned to practice after missing the Texans' last game with a sprained ankle and foot.
"[Schaub] is obviously disappointed," Kubiak said. "I wouldn't expect anything else.
"We talked for a long time. He's a competitor. He wants to be the guy in there. I know it's very difficult on him. It's very difficult on me, too."
Kubiak said he informed both Keenum and Schaub of his decision last week before the Texans broke for their bye week.
"Obviously very disappointing for me after all we've been through here and all we've accomplished and done," Schaub said. "But I'm part of the reason that we're in this situation as a football team, so it's his decision. He's the head coach. Obviously as a player and competitor, I don't like it. I want to be out there."
Keenum said that the bye week was a welcomed break.
"It was good to be able to rest and reload a little bit and still have the mindset of being ready to go," Keenum said. "Really resting my body, but keeping my mind sharp. Continue to watch film. It was good."
Keenum was active for the first time in his NFL career two weeks ago against the Kansas City Chiefs. The Texans lost 17-16, but Kubiak said Keenum's play provided a spark.
That spark was why Kubiak elevated Keenum ahead of T.J. Yates, who entered the season as Schaub's backup.
In his first start against the Chiefs, Keenum opened up a deep passing game that the Texans had moved away from lately. According to ESPN Stats & Information, he completed three of five pass attempts longer than 20 yards, including one for a touchdown to DeAndre Hopkins. In the previous four weeks, the Texans had attempted only six such passes total.
He finished with a passer rating of 110.6, completing 15 of 25 passes for 271 yards and a touchdown. He was sacked five times -- all in the second half -- by perhaps the best defense in the NFL.
Schaub struggled before the injury he suffered on Oct. 13. He became the first quarterback in NFL history to throw interceptions that were returned for touchdowns in four consecutive games.