The soldier was wounded when an improvised bomb detonated near the town of Jalalabad in Nangarhar Province on Monday, the US military said in a statement.
Fighters then attacked the patrol with small arms, it said.
The patrol returned fire, killing one fighter and capturing three more, it said, adding that the wounded soldier returned to duty after treatment.
Another improvised bomb detonated near a US patrol in the south-eastern province of Paktia on Monday, damaging a vehicle, but causing no casualties, the US military said.
The attack in Nangarhar came a day after the US military said it had killed four fighters and captured several in raids on al-Qaida-linked compounds in the Jalalabad area at the weekend.
A 17,000-strong US-led force is in
Afghanistan fighting the Taliban
It said those killed and captured included some Arabs.
Taliban and allied fighters have been waging a guerrilla war against a 17,000-member US-led force and the Afghan government since being overthrown in 2001.
Some non-Afghan fighters have stayed in the country to help the Taliban and have also mounted attacks from remote tribal areas across the border in Pakistan.
US officials say they believe Usama bin Ladin is hiding in the rugged borderlands between Afghanistan and Pakistan.