"The militants launched the attack on the police station in the city at around 5.30 am," the official told Xinhua.
"The force of the car bombing destroyed the station building and damaged several other buildings around, including governor house and the local national TV office building. More than five militants were involved in the pre-dawn attack," he added.
Jalalabad is the capital of the eastern Afghan province of Nangarhar.
The official said sporadic firing could still be heard in the area. Four militants were among those killed while the majority of the injured people were policemen.
Shortly after the incident, the Taliban claimed responsibility.