Bush's chief of staff, Jean Becker, said the 88-year-old checked in last Friday. Bush's office released a statement saying he has been in and out of the Methodist Hospital in the Texas Medical Center with complications related to bronchitis.
Becker said the illness is not life-threatening, but there were some earlier concerns that it could develop into pneumonia.
He is reported to be in stable condition and doctors hope to release the former president by this weekend.
Bush was seen recently attending a Houston Texans NFL game, something he does frequently. He has a form of Parkinson's disease, forcing him to use a wheelchair or motorized scooter to get around.
Bush and his wife, Barbara, make their winter home in Houston and spend summers in Kennebunkport, Maine. Their son, former President George W. Bush, and his wife have been among the elder Bush's visitors.
