The team said that Kubiak is expected to make a full recovery and did not give a timetable on his return to the sidelines.
Kubiak collapsed while leaving the field at halftime of Sunday night's 27-20 loss to the Indianapolis Colts.
A transient ischemic attack, or warning stroke, occurs when blood flow to the brain is interrupted briefly, and is caused typically by a blood clot or narrowed blood vessels.
Kubiak also released a statement Tuesday.
"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 the statement. "I've been through an ordeal, and my focus now is to get back to good health.