Pillay also urged Israel to allow the flow of aid including food, medicine and fuel to resume, and to restore electricity and water services in Gaza.
She said that “1.5 million Palestinian men, women and children have been forcibly deprived of their most basic human rights for months”.
An Israeli defence ministry spokesman said that continued rocket fire from Gaza towards Israel had prompted the decision to close the crossings again.
Humanitarian aid groups have warned that the Gaza Strip is dangerously short of essential supplies, despite the delivery of aid on Monday.
Sherine Tadros, Al Jazeera’s correspondent in Gaza, said the latest closures had blocked the delivery of about 17 truckloads of aid to UN Relief and Works Agency (Unrwa) distribution centres in the Gaza Strip.
According to Unrwa, the 11 truckloads they received on Monday will be enough to continue distribution to the 750,000 Palestinians in Gaza for about a week, our correspondent said, adding that the UN did not know what it could do after that.
Oxfam International, a British humanitarian agency, said in a statement that “only the bare minimum of goods have entered Gaza in the past couple of days”.
The organisation “fears a serious worsening once again of the humanitarian situation if urgent action is not taken”, Barbara Stocking, Oxfam’s chief executive, said on Tuesday.
Before allowing some aid trucks into Gaza on Monday, Israel had not allowed relief workers to deliver aid to Gaza since November 4.
In the past few days, Israel has also cut off fuel supplies into Gaza, forcing the closure of the territory’s main power plant.
The Israeli-imposed restrictions follow a series of Israeli raids into Gaza, in which more than a dozen Palestinian fighters have been killed.
Several Israelis have been injured by rockets fired by Palestinian fighters into Israel in recent days.
Hamas fighters fired mortar bombs at Israeli soldiers who were searching for explosives near the Gaza border on Tuesday, Israel’s military and Hamas said.
Also on Tuesday, Israeli tanks entered about 400 metres into the Gaza Strip, east of the city of Rafah, residents and Gaza security officials said.