A statement issued by the group and quoted by the news agency said it would provide details later.
There was no confirmation of the claim from any official source and the army did not say where the alleged incident took place.
Israeli media reported that the army had confined soldiers to their bases and were checking for missing soldiers.
The massive security operation highlights Israel's fears of having more soldiers kidnapped.
Israel already has one soldier being held captive. Gilad Shalit was captured by Hamas-allied fighters three years ago in a cross-border raid from Gaza.
Shalit has not been seen since then, and the Red Cross has not been permitted to visit him.