Police said the officer was among those who responded to a report of a shoplifter at a Lincoln grocery store before dawn Friday morning.
Police say the 30-year-old suspect fled when officers arrived. Officers gave chase, and the suspect turned around and punched officer closing on him.
The officer, who has not been named, was taken to a local hospital for treatment of a broken nose.
The suspect is behind bars on suspicion of theft and felony assault of a police officer.