The full effects were not immediately clear but the arid territory's desalination plants receive power for producing drinking water.
Israel last week cut off all supplies of goods to the territory of more than two million people, in an echo of the siege it imposed in the earliest days of its war with Hamas.
It seeks to press the militant group to accept an extension of the first phase of their ceasefire, which ended last weekend.
Cohen posted on X a picture of him signing the order, which is effective immediately, writing: "Enough talk, it's time for action".
Israel wants Hamas to release half of the remaining hostages in return for a promise to negotiate a lasting truce.
Hamas instead wants to start negotiations on the ceasefire's more difficult second phase, which would include the release of remaining hostages from the Gaza Strip, the withdrawal of Israeli forces and a lasting peace.
Israel says Hamas has 24 living hostages and the bodies of 35 others.
The militant group - which has warned that cutting off supplies to the Gaza Strip would affect the hostages as well - said on Sunday it wrapped up the latest round of ceasefire talks with Egyptian mediators without changes to its position, calling for an immediate start of the ceasefire's second phase.
Israel had warned when it stopped all supplies that water and electricity could be next.
The new letter from Israel's energy minister to the Israel Electric Corporation tells it to stop selling power to the Gaza Strip.
The coastal territory and its infrastructure have been largely devastated by the war, and generators and solar panels are used for some of the power supply.
The electricity cut also could affect water pumps and sanitation.
Israel has faced sharp criticism over cutting off supplies to the Gaza Strip.
"Any denial of the entry of the necessities of life for civilians may amount to collective punishment," the United Nations human rights office said on Friday.
The ceasefire has paused the deadliest and most destructive fighting ever between Israel and Hamas, sparked by the Hamas-led attack on southern Israel on October 7, 2023.
The first phase allowed the return of 25 living hostages and the remains of eight others in exchange for the release of nearly 2000 Palestinian prisoners.
The White House on Wednesday made the surprise confirmation of direct US talks with Hamas.
On Sunday, US envoy Adam Boehler told CNN that "I think you could see something like a long-term truce, where we forgive prisoners, where Hamas lays down their arms, where they agree they're not part of the political party going forward. I think that's a reality. It's real close".
When asked if he would speak with the militant group again, Boehler replied "You never know".
He added: "I think something could come together within weeks" and expressed hope for a deal that would see all hostages released, not only the US ones.
Hamas on Sunday reiterated its support for a proposal for the establishment of an independent committee of technocrats to run the Gaza Strip until Palestinians hold presidential and legislative elections.
Taher Al-Nono, political adviser to the leader of Hamas, confirmed the talks with the US, saying the discussions had taken place in the Qatari capital over the past week.
"Several meetings have already taken place in Doha, focusing on releasing one of the dual-nationality prisoners. We have dealt positively and flexibly, in a way that serves the interests of the Palestinian people," Nono told Reuters.
He added that the two sides had also discussed how to see through the implementation of the phased agreement aimed at ending the Israel-Hamas war.
"We informed the American delegation that we don't oppose the release of the prisoner within the framework of these talks," Nono said.
Hamas' attack in October 2023 killed about 1200 people, mostly civilians, inside Israel and took 251 people hostage.
Most have been released in ceasefire agreements or other arrangements.
Israel's military offensive has killed more than 48,000 Palestinians in the strip, mostly women and children, according to Gaza's Health Ministry, which does not say how many of the dead were militants.
with Reuters and DPA
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