Gun battles started early on Thursday morning in Jalalabad after a "multi-pronged" attack by insurgents.
Police said they shot dead seven attackers, all of them wearing suicide bomb vests.
The attack comes after the Taliban vowed to disrupt the run-up to presidential elections in the country on 5 April.
"Ten policemen, including the district police chief, were killed and 14 police were wounded," deputy interior minister Mohammad Ayoub Salangi told AFP.
"One civilian was also killed, and all seven attackers."
The Taliban claimed responsibility for the attack in a text message sent to media.
The insurgents are believed to have stormed Jalalabad's key police station, close to government offices and the headquarters of the governor, shortly after a car bomb was detonated.
The gun battles continued for several hours after the bomb blast and Nato sent helicopter gunships to support Afghan security forces.
Interior ministry spokesman, Sediq Sediqqi, said one or two attackers had holed up in a small room inside the police station before they were finally killed by security forces.
Witnesses in the city told the BBC that the state-run Radio Television Afghanistan was one of many buildings that were still on fire following the attack.
Mohammad Habib, an eyewitness, said the explosion shook the city.
"I woke up and my windows were broken. Then there were gun shots and explosions throughout the morning. Now almost half of the city remains closed," he said.
Local taxi driver Khan Jan told the BBC: "The sound of the explosion was deafening, there was a powerful explosion which broke windows of nearby shops and homes. It woke the city."
On Tuesday, a suicide attack in northern Afghanistan killed 17 civilians including women and children and injured more than 60.
The Taliban have threatened a campaign of violence to disrupt the election on 5 April.
The poll will choose a new Afghan president to lead the country as foreign troops prepare to end their combat mission by the end of the year.
Taliban fighters have killed at least 10 policemen in an attack on a city in eastern Afghanistan.