The rights groups petitioned the court, the highest legal authority in Israel, to reverse the sanctions, calling them an "illegal" act of collective punishment against the 1.5 million Palestinians who live in the territory.
Menachem Mazuz, Israel's attorney general, will also review a decision taken by Ehud Barak, the defence minister, to enforce periodic electricity cuts on the Gaza Strip, his office said.
Israel began restricting fuel shipments to the strip on Sunday, as part of a series of sanctions in the face of Palestinian rocket attacks.
The move comes after Israel declared the territory, run by Hamas since June, a "hostile entity" on September 19, paving the way for further sanctions and restrictions.
Gaza is entirely dependent on Israel for trade and following the Hamas takeover, Israel and Egypt closed their borders with Gaza.
Israel allows only basic items, such as food and medicine, into the territory.