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.
Dutch Foreign Minister Sigrid Kaag has tweeted her thanks to Qatar, saying that 13 Dutch nationals were on board the flight.
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 August15.
More than 124,000 foreigners and Afghans fearful of Taliban retribution were flown out of the country.
Around 100 US citizens were thought to be left in Afghanistan before the flight.
Photos have also emerged showing injuries inflicted on two journalists who covered protests on Wednesday.
They are reported to have been badly beaten after being arrested by the Taliban in Kabul.
“One of the Taliban put his foot on my head, crushed my face against the concrete,”photographer Nematullah Naqdi told AFP news agency. ”They kicked me in the head… I thought they were going to kill me.”
Mr Naqdi was covering a protest by women in front of a police station with his colleague at the local Etilaatroz newspaper, Taqi Darybai.
The Taliban have banned protests unless authorised by the justice ministry.
But dozens of demonstrators chanting “we want freedom” gathered near the Pakistan embassy in Kabul and Taliban gunmen opened fire to disperse them, protesters said.
Local media have also reported another protest by women in Kapisa province, north-east of Kabul. Sources told Aamaj news that several women had been arrested.
“It is our right to protest,” said Haseeneh from Kabul. “Now that we know what the Taliban meant by their new cabinet, we will protest. They kept saying that women should wait till the Taliban announce their new cabinet. There is no single woman in the cabinet.” -AFP