The attack is the latest to hit American forces amid an ongoing, US-led drive to forge a peace deal in Afghanistan, more than 17 years after the Taliban were ousted.
According to Nato, the blast also wounded three US troops in what is the deadliest attack on American forces in Afghanistan so far this year.
Officials did not immediately release the names of those killed, or the nationality of the contractor.
"The wounded service members were evacuated and are receiving medical care," Nato said in a statement.
Earlier, the Taliban claimed to have conducted the attack, saying 'multiple invaders' had been killed. They added that one armoured personnel carrier had been 'completely destroyed.'
Taliban kill 12 Afghan security forces in western Afghanistan
The blast brings to seven the number of US troops killed in Afghanistan so far this year.
Still, American casualties have fallen dramatically since the end of 2014, when Afghan forces took over from US-led Nato combat troops to secure the country.
The US now has some 14,000 troops in Afghanistan, most of them deployed to train and advise Afghan counterparts.
While parts of Afghanistan including Kabul have experienced something of a lull in attacks in recent weeks, US and Afghan forces have stepped up attacks on the Taliban across the country.
Bagram, America's largest air base in Afghanistan, is located about 50 kilometres north of Kabul.
Earlier, Bagram district governor Abdul Shakoor Quddusi said a car bomber attacked an armoured vehicle carrying foreign forces close to a gate to the base.
"The area is closed down by foreign forces and we don't have any information of any possible casualties," Quddusi told AFP.
Afghans, meanwhile, are on high alert for a new round of violence when the militants kick off their expected spring offensive.
They typically declare a new fighting season as winter snows melt, and have in the past sought to gain control of district centres and to target government facilities.
Taliban leaders are set to meet with Afghan officials in Qatar next week for a fresh round of talks as the US tries to broker a peace deal.
Last week, US envoy Zalmay Khalilzad called for a "comprehensive and inclusive" intra-Afghan dialogue between the government, women, youth and civil society.
The Taliban has until now refused to meet with the Kabul government, accusing it of being a puppet regime.
The diplomatic spat between Washington and Kabul came to a head last month when Afghanistan's national security adviser Hamdullah Mohib accused Khalilzad of a lack of 'transparency', even suggesting the Afghan-born envoy wanted to be 'viceroy' of his native country.
Washington reacted furiously, with US officials reportedly refusing to attend meetings in which Mohib was present. The outspoken adviser visited eastern provinces when Khalilzad was in Kabul.
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