"After the important role the War Media Centre has played on various fields, Facebook and Twitter administrators have blocked its pages without notice," the centre's account on Telegram said.
The statement added that the move was part of the social media platforms' "efforts against the media of the resistance".
The move came after Israel's public security minister sent a letter to Twitter last month warning it could face prosecution if it does not block accounts belonging to Hizballah and Palestinian Islamic movement Hamas.
Israel fought a devastating war against Hezbollah in Lebanon in 2006 that killed more than 1,200 Lebanese, mostly civilians, and 120 Israelis, most of them soldiers forcing Israeli troops out of Lebanon.
Last month, Israel launched a large-scale attack on what it said were Iranian targets in Syria, raising fears of a major confrontation.
Israel has long called for Iranian-backed forces such as Hezbollah to keep away from its border with Syria.