The officer spotted an old pickup truck leaving the rear of the building with a safe dangling from a winch in the bed of the truck.
The officer attempted to stop the driver of the truck, who then, according to police, drove at the officer. The officer pulled his gun and opened fire, causing the driver of the truck to hit a curb. The crash disabled the vehicle and the two men bailed out and escaped on foot. The pair remain at large.
Dallas County sheriff's spokeswoman Kim Leach said the officer wasn't injured and that the condition and a description of the men is not available. Leach added that she wasn't aware of the contents in the safe.
The Sixth Floor Museum, which chronicles the final days and assassination of President John F. Kennedy, was closed Tuesday while the investigation into the robbery attempt was under way.
The museum's spokesperson, Deborah Marine, said all of the museum's collections and artifacts were safe and secure.
Anyone with information about the incident is asked to call the Dallas County Sheriff's Department.