The militants were shot dead when they stormed the police base in Sarobi district, 50 kilometres east of Kabul, after another suicide attacker died when he exploded a vehicle bomb outside the entrance.
Taliban insurgents claimed responsibility for the two-hour attack, which occurred in the same district where presidential candidate Abdullah Abdullah's convoy briefly came under gunfire on Wednesday.
"Today at about 6:20 am, a suicide bomber driving a minivan detonated himself at the entrance gate of the Sarobi police headquarters," General Mohammad Zahir, Kabul province's police chief, told AFP.
"As a result of the attack, one officer was killed and three others were wounded."
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Male militants have previously used the all-enveloping burqa to disguise themselves and evade security checks in Afghanistan, including in a 2012 attack when four French troops were killed.
Taliban spokesman Zabihullah Mujahid said the insurgents, who were ousted from power in 2001, were behind Friday's attack.
"The mujahideen fighters were equipped with heavy and light weapons and suicide vests, and caused heavy casualties to the enemy," he said in an emailed statement.
Afghanistan goes to the polls on April 5 to select a successor to President Hamid Karzai, as some 55,000 US-led combat troops pull out of the country after 13 years of battling the fierce Taliban insurgency.