Search and rescue teams are still combing through the rubble left behind after the tornado hit the city on Saturday, Efe news quoted the Mayor as saying.
The injured were transported to hospitals, White said, without providing figures on the number of people hurt.
The tornado hit the city at around 10.30 p.m. and moved across El Reno on a southwest to southeast track.
Media reports said the deaths occurred at a mobile home park in the small city.
"It's a tragic scene out there," White said. "People have absolutely lost everything."
The tornado levelled a motel and television stations aired video of emergency services personnel digging through the rubble.
The Weather Channel, meanwhile, reported that another tornado hit Tulsa, the second-largest city in Oklahoma, causing property damage.
PowerOutage.us, a website that tracks power outages across the country, said about 37,000 customers were without electricity on Saturday night in the affected areas.
Last week, tornadoes affected several states in the Midwest, killing at least three people in Golden City, Missouri.