The airports closed on Sunday.
A limited amount of domestic service will resume at Houston's Hobby Airport and George Bush Intercontinental Airport starting at 4 p.m. Wednesday, according to a news release posted on the Facebook page for George Bush Intercontinental Airport. Full service, including international flights, is expected to resume by the weekend.
The post warned that many of the roads around the airport continue to be impassable because of flood waters and advised all passengers to add extra travel time.
Airlines canceled several thousand flights over the weekend, and both airports had fully shuttered by Sunday afternoon.
The storm has been battering the city for days, destroying 30,000-40,000 homes and killing 30 people. The storm moved into Louisiana, making another landfall early Wednesday morning, The New York Times reported.