One assailant broke the passenger-side window with his gun and took the two men away. A driver and bodyguard were left unhurt, the official said. The kidnappers were wearing military uniforms, the official said, but not the design and color of the official Afghan army uniform.
There has been no claim of responsibility.
The US Embassy in Kabul confirmed that an American citizen had been kidnapped near the university.
Embassy security officials are working with Afghan law enforcement and the school to assist in the investigation into the kidnapping, embassy spokeswoman Susan C. Doman said.
A spokesperson at the Australian Embassy in Afghanistan has confirmed "the apparent kidnappping of an Australian in Kabul."
"We continue to advise Australians not to travel to Afghanistan because of the extremely dangerous security situation, including the serious threat of kidnapping," the spokesperson said.
Both the US and the Australian officials said they can't give more precise details because of "privacy" concerns.
Officials at the university could not be immediately be reached for comment.
The school said on its Facebook page that its Kabul campuses will remain closed Monday and Tuesday but did not explain why. Regional centers are operating as normal, the Facebook page said.
Attack last week injured tourists
The tourists were from the United States, Ireland, Britain and Germany.
Many countries, including the US and UK, have longstanding travel advisories warning against all but essential travel to Afghanistan due to the security situation throughout the country.
Two foreign aid workers with the International Assistance Mission were killed in the city of Herat in 2014.
Heightened security fears
Violence has erupted across the central Asian country this spring and summer.
And a rash of kidnappings and Taliban bombings have heightened security fears in Kabul. US and other diplomats have been barred from traveling by road the short distance from the city's international airport to their diplomatic missions. Instead, they've been ferried by helicopter.
CNN's Andreena Narayan, Sandi Sidhu and Catherine Treyz contributed to this report