"The secretary general is saddened with the loss of life and sends his condolences to the government and people of the United States and hopes the injured recover quickly", Stéphane Dujarric said in a communiqué.
Harvey, which has now been downgraded to a tropical storm, is the most powerful hurricane to hit the USA since 2005 and the worst to reach Texas since 1961.
The storm has killed at least 10 people and 17,000 have had to seek shelter according to local authorities.