The attack occurred as the troops were driving in an armored vehicle in Kunar province near the regional capital Asadabad, Sgt. Maj. Larry Lane, a military spokesman, said.
The two wounded were evacuated to a base in Asadabad and one had already been treated and released, he said.
Provincial Gov. Assadullah Wafa said the bomb had been detonated by remote control. He blamed "enemies of Afghanistan" for the attack, a term commonly used to refer to Taliban rebels.
Kunar is a mountainous province on the border with Pakistan and scores of militants are believed to hide out there.
Some of the deadliest attacks on U.S. forces this year have occurred in Kunar. In June, suspected Taliban rebels shot down a special forces helicopter, resulting in the deaths of 16 troops, after killing four American commandos on the ground.
Meanwhile, another U.S. soldier was killed and four others hurt when their armored vehicle rolled over in the country's south Wednesday, the military said.
The troops were conducting a combat operation near Kandahar city, a former Taliban stronghold, when the accident occurred, a U.S. military statement said.
"Enemy activity was not a factor," it said.
The injured soldiers were rushed to the hospital at the Kandahar Airfield, the U.S.-led coalition's local headquarters. Three of the injured were treated and released while the fourth was flown to an unspecified location for further treatment, the statement said.
The cause of the accident was under investigation.
The deaths brought to 208 the number of U.S. troops killed in and around Afghanistan since American-led forces ousted the Taliban in late 2001 for harboring al Qaeda leader Osama bin Laden.
The names of the victims were withheld pending notification of next of kin.