Videos of Palestinians stabbing Israelis or calling for such attacks as well as footage of rioters throwing stones at Israeli soldiers have been shared on the Internet.
Others showing Israeli officers shoot dead alleged attackers have also helped galvanise Palestinian youths, with violence since the start of the month leading to warnings of the risk of a full-scale uprising, or third intifada.
It was unclear which videos Israel requested be removed or how many.
"Several videos, particularly from Hamas, that are inciting violence, hate and the murder of Israelis and Jews were removed after we made the request with YouTube," foreign ministry spokesman Emmanuel Nahshon told AFP.
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He said Israel made the request by letter to the Israeli branch of Google, which owns YouTube.
"These videos describe terrorist attacks, justify their culprits and present Jews and Israelis in a hateful and racist manner," he said.
According to Nahshon, YouTube did not respond directly "but we were able to note that the videos in question were quickly erased".
Israeli officials are to meet Facebook representatives on Tuesday to make a similar request.
The ministry has set up a department to monitor social networks and also called on Israelis to report such videos to YouTube and Facebook.