Dostum, who who had fled to Turkey amid allegations of torture and abuse, left the airport minutes before the explosion. He was riding in an armored vehicle.
At least 11 people were killed and 14 people wounded in the blast, Kabul police spokesman Hashmat Stanekzai told the BBC. Interior ministry spokesman Najib Danish told Al Jazeera said a child and security force members were among the casualties.
Stanekzai said a bomber on foot set off his explosives outside the gate of the airport, where supporters awaited Dostum as his motorcade passed.
Dostum arrived in a chartered plane from Turkey where he has lived since May 2017. He denied accusations he ordered his men to kidnap and rape a political rival.
Before his return, Dostum's supporters had forced the closure of election and government offices, and blocked sections of highways.
In 2001, he helped the United States oust the Taliban.