Doctors diagnosed the problem as a transient ischemic attack, often called a mini-stroke, which is something that occurs when blood flow to the brain is briefly interrupted.
Kubiak suffered the attack while leaving the field at half time of the match against the Colts at the weekend. The Texans led 21-3 at the halfway stage but went on to lose 27-24 after hearing of their head coach's health scare.
A return date has not yet been set for Kubiak, but the 52-year-old is expected to make a full recovery.
The Texans have not named an interim coach for Sunday's match against the Arizona Cardinals as they look to end a six-match losing streak.