The MoD said processing facilities at the Baron Hotel, outside the capital’s airport, had been closed.
The defence secretary expressed “deep regret” that not everyone eligible had been evacuated, including around 800 to 1,100 Afghans and 100 to 150 Britons.
On Friday morning, the MoD said 13,708 people had been evacuated by the UK from Kabul under Operation Pitting, which began on 13 August.
Mr Wallace said this included nearly 8,000 Afghans eligible under the UK’s relocation scheme for those who worked for the UK government and other vulnerable individuals, as well as 4,000 British passport holders.
Others evacuated include embassy staff and nationals from partner nations.
The defence secretary said the operation was “a remarkable achievement” in a “very hostile environment”.
But he told LBC Radio around 800 to 1,100 eligible Afghans would be left behind, as well as approximately 100 to 150 British nationals, some of whom he said were staying willingly.
Mr Wallace told BBC Breakfast that between eight and nine additional flights would come into Kabul to evacuate around 1,000 people who remained inside the airfield.