Hassan Khanzada and Syed Munir Shah were at a Kabul market on Wednesday when they were picked up by members of the National Directorate of Security, the intelligence agency of Afghanistan, media reports said.
They were taken to a detention centre along with the embassy's official vehicle, Dawn reported.
Khanzada, a visa assistant at the embassy, was "manhandled", it said.
Shah is a staff driver at the embassy.
The Pakistan embassy approached the Afghan Foreign Ministry and sought their immediate release.
On Wednesday, Pakistan's Foreign Office summoned the Afghan Deputy Head of Mission, Zardasht Shams, and lodged a protest over the incident.
Dawn said the incident had dealt another blow to the already fraught ties between Pakistan and Afghanistan.
The incident took place amid efforts by the US-led coalition in Afghanistan to mend fences between Islamabad and Kabul in the aftermath of border clashes in which about a dozen lives were lost.
Dawn said there were serious concerns about the safety and security of Pakistani diplomats and embassy staff in Kabul.