Bildt, who was accompanied by UN Secretary General Ban Ki-Moon, spent the night at the US military's Bagram airbase to the north of the Afghan capital. Bildt and Ban were on their way to an international ministerial conference on the future of Afghanistan when the attack took place.
The foreign minister wrote on his blog that they were around one kilometre from the runway when forced to divert.
“It naturally created quite an uncertain situation,” he said.
Bildt and Ban were unable to leave Bagram for several hours before heading to the Kabul conference, where participants include US Secretary of State Hillary Clinton.
“After the night's drama, the UN's Secretary General Ban Ki-Moon and I - and our colleagues - finally at four a clock in the morning were able to descend in darkness in two helicopters into the ISAF area in central Kabul,” Bildt wrote.
“That the Taliban and others should try to destroy this important conference was naturally expected. Our presence here in the centre of Kabul is a demonstration of our support for the peace and stabilization process in this country.”
But the minister insisted that the rocket attack had not caused serious disruption in the end:
“It was not much more than a serious attack on our night's sleep,” he wrote.
Swedish Foreign Ministry spokesman Anders Jörle had on Tuesday was unable to say whether anyone had been hurt in the attack on the airport or which groups might be responsible.
Danish foreign minister Lene Espersen was among others forced to delay trips to Kabul due to the attack.