The injured soldiers were taken to a nearby hospital in Saioun city, a hospital source told AA.
A military official who spoke on condition of anonymity told AA that "terrorists" had targeted the patrol with a roadside bomb.
Authorities have yet to comment on the attack, for which no group has yet claimed responsibility.
In recent months, Hadhramaut has witnessed frequent militant attacks, which the government typically blames on the Al-Qaeda-linked Ansar al-Sharia group.
According to the government, Al-Qaeda remains active in several parts of the country's south, from which it stages sporadic attacks on army and police personnel.
Yemen has remained in a state of turmoil since pro-democracy protests forced autocratic president Ali Abdullah Saleh to step down in 2012 after 33 years in power.