This comes as the U.S. significantly withdraws its presence in the Middle East.
The U.S. military spokesman in Baghdad had confirmed earlier that 14 rockets had been fired towards the base with some landing inside the perimeter.
Separately, a defense official said that the injuries consist of a concussion for one of the service members and an abrasion for the other.
This comes more than a week after White House officials said the U.S. carried out an airstrike near the Iraq-Syria border to target Iran-backed militias and two facilities behind drone attacks on U.S. troops in Iraq.
This is a developing story. Please check back for updates.