The violence came a day after fighting between rival neighborhoods in the city caused four other deaths, officials said.
The soldier was killed by sniper fire, The (Beirut) Daily Star reported.
"The army forces were shot while fulfilling their mission, which led to the killing of one soldier and the wounding of others," the statement said.
Much of the fighting was between supporters and opponents of Syrian President Bashar Assad, whose country is engulfed in a civil war.
"It was a horrible night ... My family and I had to hide under the beds," said 26-year-old Ghofran Nabulsi, who lives in the Qibbeh area. "I could hear gunshots all through the night. Each time I would hear shooting, I would feel that bullets were going to pierce the window of my room."
"Expanded Army raids in the city led to the arrest of a number of gunmen and the confiscation of arms and ammunition," the military's statement said.