The four people, whose identities were not immediately clear, were kidnapped at gunpoint in Maiwand district in the southern province of Kandahar, Qari Mohammad Yousuf, a spokesman, said.
"The four Albanians were travelling in two vehicles when our Mujahideen [holy warriors] kidnapped them," Yousuf said by satellite phone from an undisclosed location.
Government officials in Kandahar and in Kabul said they had not heard about the report.
Yousuf said the fate of the four would be decided by Mulla Mohammad Omar, the Taliban's fugitive supreme leader.
The Taliban have been fighting the US-backed government of Hamid Karzai, the president, and anyone supporting it since US-led forces overthrew the Taliban in late 2001.
In the past, insurgents have killed several foreigners, including a British national involved in road projects, after kidnapping them.
The Taliban and their allies, including fighters from Osama bin Laden's al-Qaida network, are mostly active in the southern and eastern parts of Afghanistan close to the border with Pakistan.
"The four Albanians were travelling in two vehicles when our Mujahidin [holy warriors] kidnapped them"
Qari Mohammad Yousuf,
Nearly 70 foreign soldiers, most of them Americans, have been killed in the Taliban-inspired insurgency in the past year in Afghanistan, the bloodiest period since the Taliban were ousted.
US-led forces invaded Afghanistan to overthrow the Taliban government after its leader refused to hand over Bin Laden, architect of the 11 September attacks on the United States.