According to Odessa Police Department, one shooter was killed and "the threat has been contained", Xinhua news agency reported on Saturday.
Odessa Police Department earlier sent a Facebook alert on the active shooting, saying "At this time there are multiple gunshot victims. The suspect just hijacked a US mail carrier truck." It also urged people to get off the road and "use extreme caution."
Odessa is about 30 km southwest of Midland, which is a city in western Texas. Part of the Permian Basin area, it is an oil industry centre.