Out of the three, one was in critical condition and was airlifted to the Army Hospital in Srinagar, a senior official said.
Terrorists attacked the convoy near Kralgund in Handwara town. Army launched the counter-offensive but terrorists managed to escape.
Army has launched cordon and search operations in the area.
This is the second terrorist attack on army convoy in the Valley since the July 8 killing of Hizbul Mujahideen terrorist Burhan Wani.
Last month, two soldiers and a policeman were killed and five soldiers injured when an army convoy was attacked on the Srinagar-Baramulla highway near Khawaja Bagh in Baramulla.