"I believe my assessment is that it is not effective; it's not efficient, and it puts our troops at greater risk," said U.S. Army General Stephen Townsend.
The individual killed in the Thursday drone strike was allegedly attempting to plant explosive devices alongside a Somali road.
Images of the explosions show sheared metal and extensive damage to buildings.
China's new military base is just a few miles from the only permanent U.S. outpost in Africa.
Around 100 U.S. troops ended a six-year mission earlier in 2017 after failing to capture Kony, whose group has co-opted tens of thousands of children into conflict.
President Trump gave U.S. forces in Somalia more leeway to strike the Al-Qaeda affiliate earlier this year.
Obama has tried to turn the U.S.-Africa relationship from dependency to partnership.
Al-Shabab says its fighters killed five soldiers in the clashes, a claim Nairobi denies.