Kubiak suffered a transient ischemic attack, commonly known as a mini-stroke, while leaving the field at half time of the Texans' eventual 27-24 defeat to the Indianapolis Colts on Sunday.
"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."
Kubiak is not expected to return to the sidelines in time for Sunday's match against the Arizona Cardinals despite the Texans not having named an interim head coach yet.