One of the main concerns is over possible hostage videos being shared which they say could cause distress.
The warnings are circulating not just in Israel itself but also in the US and UK - with some some singling out TikTok and Instagram in particular.
Footage of civilians being killed has been shared online.
A number of schools in Tel Aviv have been communicating the message to parents since the weekend.
Elsewhere a school in New Jersey in the US sent an email to parents suggesting they tell their kids to delete their social media platforms.
