The attack occurred near Kandahar city, a former Taliban stronghold, on Friday, but was only reported by the US military on Saturday.
About eight fighters opened fire at the patrol after it was hit by the bomb, the statement said.
Three of the fighters were detained. The two wounded soldiers were taken to a nearby base for treatment and were in stable condition.
The attack came shortly after US and Afghan forces backed by helicopter gunships killed 14 suspected Taliban fighters in central Uruzgan in the heaviest clashes since landmark parliamentary elections went off without major disruption a week ago.
One Afghan soldier died and a US soldier was wounded in the fighting.
It was the first time US-led forces used air power since President Hamid Karzai questioned the need for airstrikes.
The spate of violence followed warnings by a top US general that the Taliban’s insurgency was likely to continue well into next year after a winter respite.