The two countries were due to play three ODI matches in early September in Sri Lanka, but the Pakistan Cricket Board (PCB) said late on Monday that the Afghanistan Cricket Board had requested the series be postponed.
"PCB has accepted ACB's request to postpone next month's ODI series due to players' mental health issues, disruption in flight operations in Kabul, lack of broadcast facilities and increased COVID-19 cases in Sri Lanka," the PCB tweeted.
"Both boards will try to reschedule the series in 2022."
With commercial flights from Kabul airport yet to resume, media reports said the Afghanistan team had been looking to travel to Pakistan by road and fly to Colombo via Dubai.
But the logistical challenges increased after Sri Lanka last week announced a 10-day lockdown to curb the spread of COVID-19, as surging infections and deaths overwhelm the island's health system.
The Taliban have said they would not interfere with men's cricket in the country, Afghanistan's biggest sporting success of recent years. The fate of the women's programme, however, remains unclear.