Lt. Col. Eyal Weiss, 34, commanded the Duvdevan unit which swept through the Palestinian-ruled West Bank village of Saida in a search for militants.
"Weiss was killed when the wall of a home that had been demolished earlier by (Israeli) forces collapsed," the army said in a statement.
The soldiers killed one militant in Saida, northeast of the town of Tulkarm, after coming under fire, the army said earlier. Palestinian sources said the troops detained 13 people in the village and demolished a house belonging to a militant.
Weiss had commanded Duvdevan since April. Its members often disguise themselves as Palestinians during undercover operations against militants.