Police initially responded to a call about a possible bomb inside a moving truck in the parking lot at the driveway shortly before noon. 21.30 (22.30 ET) and then received other calls about a shooting, the statement said.
Two of the victims were transported to the University of Nebraska Medical Center while the other two were pronounced dead at the scene, police said.
Authorities do not identify the victims until their families have been notified.
Lieutenant Andy Jashinske said there was a moving vehicle in the Sonic parking lot, but no bomb was found and police said there is no indication that there are other suspects involved.