“There is no active shooter at this time. All agencies are investigating reports of possible suspects.”
Earlier, police believed there may have been two shooters because separate vehicles were used by the gunmen. They later clarified that there was only one shooter.
People in Odessa were instructed to “get off the road and use extreme caution”, according to a Odessa Police Department post on Facebook.
The police department of Midland, Texas, about 30 kilometres north-east of Odessa, said there were two shooters in two separate vehicles and also warned people to stay away from particular areas.
“We believe there are two shooters in two separate vehicles,” the department said on Facebook. It said the two vehicles are a small, gold and white Toyota truck and a US Postal Service van.
The shooting comes four weeks after 22 people were killed at a shopping centre in El Paso, Texas by a gunman who told police he targeted Mexicans.
Hours after the shooting in Texas, a gunman opened fire in a nightclub district in Dayton, Ohio, killing nine. There was no link between the two attacks.
Odessa police were to hold a news conference at 6.30 pm EDT (8.30am AEST), according to local media.