The wounded soldiers were transported to a U.S. medical facility on the airbase, 25 miles north of Kabul, for immediate medical treatment, reports CBS News' Sami Yousafzai.
The injured included four military personnel and two civilians, a U.S. military spokeswoman said. Lt. Cmdr. Christine Sidenstricker gave no more details, but a senior Afghan official at the base said the casualties resulted from two rockets fired at the airfield.
The names of the service members are being withheld pending notification of the next-of-kin, the U.S. military said in a statement issued to media.
"On behalf of the Combined Joint Task Force-82 team, we offer our condolences and sympathy to the families of our two brave service members," said the commanding general of CJTF-82.
Army Major General Curtis Scaparrotti added: "Their sacrifice in the name of security and a better way of life for the Afghan people will not be forgotten."
As a result of Sunday's losses, the number of U.S. troops killed in Afghanistan this year has soared to 80.
With the attack under investigation, it was not immediately obvious if any Afghan civilians living near Bagram were harmed as a result of the attack.
A Taliban commander Qari Talha in charge of the militant group north of Kabul, called CBS News and claimed responsibility for Sunday's attack.
He said that attacks upon alternative U.S. Army supply routes in the North and Bagram Airbase are key to the Taliban's military strategy this year.
As many as 23 people were killed in a suicide bombing outside Bagram - housing thousands of foreign soldiers - in February 2007 when former U.S. Vice President Dick Cheney was visiting the base. The attack claimed by Taliban militants had mostly killed Afghan workers.
Separately, two Afghans were killed and another 18 injured in the Pech district of the eastern Kunar province on Saturday when they were caught in the crossfire of an unprovoked insurgent attack on an Afghan National Army (ANA) outpost.
The injured were treated and evacuated by Afghan and ISAF forces. The forces were not injured in the attack in incident, which was under investigation, the alliance said.