Some 200 people, including Americans, have flown out of Kabul in the first such operation since US forces left the country.
The Qatar Airways charter flight is now en route to the Qatari capital Doha, with a second flight due on Friday.
US Secretary of State Antony Blinken urged help with evacuations during a recent visit to Qatar.
Hundreds of Afghan citizens who had helped the US military were unable to get out in last month’s US airlift.
In a press conference held at the airport, Qatari special envoy Mutlaq bin Majed Al Qahtani described Kabul international airport as operational and said it was a historic day for Afghanistan.
The flights are the first to leave since the rushed US military-led evacuations finished last month, following the Taliban takeover of the country on 15 August.
More than 124,000 foreigners and Afghans fearful of Taliban retribution were flown out of the country.
Around 100 US citizens are thought to be left in Afghanistan.