A video posted online Tuesday showed an army jeep pulling up next to the men, sitting at the roadside and smoking a water pipe in the northern West Bank village of Kafr Laqif.
As the jeep pulls away a flash and smoke can be seen in the road and the men scatter, apparently unharmed.
An army statement on Thursday referred to an investigation launched into an "incident in Kafr Laqif" but did not give details.
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"The investigation revealed that the platoon sergeant acted contrary to Israel Defence Forces standards," it said.
"The platoon sergeant and two additional soldiers present in the vehicle were sentenced in disciplinary proceedings by the battalion commander. The platoon sergeant was sentenced to military jail."
A spokesperson later told AFP that the sergeant was jailed for 10 days and the other two soldiers were confined to their base for seven days.
Stun grenades, also known as "flashbangs", produce a very loud bang and a flash of intense light, designed to temporarily incapacitate subjects without physical harm.
They can, however, cause injury if used improperly.