Taliban spokesman Zabiullah Mujahid said in a text message to journalists that one of its fighters had exploded a car bomb in Panjshir.
The insurgency has intensified terror attacks across Afghanistan to sow insecurity and weaken the government as international forces prepare to withdraw by the end of this year.
Panjshir was known as a stronghold of resistance to the Taliban's hard-line Islamic rule over Afghanistan from 1996 to 2001, when the US-led invasion toppled their regime for sheltering al-Qaeda terrorist leaders in the wake of the Sept. 11 attacks.
The province was the home of Ahmed Shah Massoud, the ethnic Tajik leader of the Northern Alliance who was dubbed “The Lion of Panjshir” for his defiance against the Soviets during the Afghan war in the 1980s and later in the anti-Taliban Northern Alliance.
Massoud was killed by two suspected al-Qaeda members posing as journalists two days before the September 11 attacks.
Presidential front-runner Abdullah Abdullah is also from Panjshir and once served as a close aide to Massoud. The Taliban hopes to disrupt security during the presidential elections, which look set for a runoff between former Foreign Minister Abdullah and ex-Finance Minister Ashraf Ghani in June.
