The Taliban claimed responsibility for the bombing, which occurred at about 10 a.m. local time, and said Cheney was the target. The vice president was unhurt in the attack, but 20 others were wounded.
Among those killed in the blast were at least one U.S. soldier, an American contractor and a South Korean soldier, NATO said.
Cheney left Bagram Air Base about two hours later for a meeting with Afghan President Hamid Karzai and other officials in the capital Kabul, and then left Afghanistan.
The vice president had spent the night at the base because his flight to Kabul had been delayed due to bad weather, reported Reuters.
The military base houses 5,100 U.S. troops and 4,000 other coalition forces and contractors. The explosion occurred near the first of three gated checkpoints visitors must pass through before entering the base.
Cheney said the attackers were trying "to find ways to question the authority of the central government," quoted the Associated Press.
White House deputy press secretary Dana Perino said she could not confirm the Taliban was behind the attack.
Militants reportedly are using the lawless Waziristan region of mountains and caves along the Afghan-Pakistan border to stage attacks on coalition forces in Afghanistan.
Cheney had earlier visited Pakistan, where he met with President Pervez Musharraf, and sent the message that cross-border attacks on Afghanistan must end or the United States may reduce aid to Pakistan, officials said.
The vice president's meeting with Karzai, meanwhile, lasted about an hour and they discussed the "problems coming from Pakistan," an Afghan government official said, according to the AP.