Kubiak collapsed while going from the sideline toward the locker room at halftime Sunday. After he was unable to stand, Kubiak was taken off the field on a cart.
Subsequent tests indicated Kubiak suffered a minor stroke. He is expected to make a full recovery but it was unclear when he would be able to return to the team.
Defensive coordinator Wade Phillips has been filling in as head coach in Kubiak's absence.
"I want to thank my family, the McNair family, the Texans organization, the doctors and staff at Houston Methodist and the entire Houston community for all the love and support we have received over the past three days," Kubiak said in a statement.
"I've been through an ordeal and my focus now is to get back to good health. Doctors have told me I will make a full recovery but we have not determined when I will be cleared to return to the office. Again, thank you for the support and concern."
Bob McNair is the majority owner of the team.
Houston has lost six consecutive games, falling to 2-6 on the season. The Texans are to play at Arizona Sunday.