An Israeli TV report revealed $127,000 of public money was spent on fitting the room on his flight to attend former UK PM Margaret Thatcher's funeral.
The expense met with anger in Israel, which is facing austerity measures.
Mr Netanyahu's office said the prime minister had been unaware of the cost.
Israeli media reports said the cost was incurred by having four walls and door installed around a double bed, and 22 business class seats fitted on a plane chartered from El Al, Israel's national airline.
The flight from Israel to the UK takes about five-and-a-half hours.
The aircraft cost about $300,000 to use, before the custom fittings. Israel's Channel 10 first reported the story, which triggered angry reactions in the media.
"Bibi is king, and in a monarchy, when the king and queen fly, price is no object," said political commentator Sima Kadmon, referring to Mr Netanyahu by his nickname, in Israel's biggest-selling newspaper Yediot Ahranot.
Mr Netanyahu's office said the prime minister needed a good night's sleep on the flight ahead of a day of busy schedules. It later said the prime minister had not been aware of the additional cost and had ordered cut-backs.
Reports said customised "rest chambers" would no longer be used on European flights, while other media quoted his office as saying they would be dropped all together.
The news came at a time when Israelis face tax rises as part of austerity measures being discussed by the cabinet.
It also follows the revelation earlier this year that the prime minister's office had an annual budget of $2,700 for ice-cream bought by his staff from a Jerusalem shop. Mr Netanyahu scrapped the allowance after the story came to light.

Dermot Nolan, chief executive of Ofgem, told the BBC that domestic gas and electricity prices should be cheaper "for the vast majority of people".
Wholesale energy costs make up nearly half of a domestic bill, and have fallen by about a third in the last 12 to 18 months, he said.
Yet, prices had not fallen, he added.
Energy UK, which represents the major energy energy companies, insisted that there was a competitive market of 34 suppliers and that people should switch for savings of hundreds of pounds.
Lawrence Slade, chief executive of the trade body, said the industry had made "mistakes in the past" in failing to assist those languishing on variable deals but that the situation had improved alongside increased competition.
The regulator has said 70% of consumers remain on standard variable tariffs which have hardly changed since early last year.
Pressure is mounting on the UK's big six energy suppliers to cut their prices in line with falling costs after the latest analysis showed wholesale gas and electricity prices in the UK hit a five-year low at the end of 2015.
Figures published on Thursday showed the cost of energy on the wholesale market tumbled to Â£36.76 per megawatt hour on the Power Index, compiled by market information provider ICIS.

The 30-year-old has played 12 times for Orient since joining in October.
"There were one or two alternative options that came up but having been here for three months and got a feel for the place, I am happy to be staying," he told the club website.
Orient, who are 21st in League Two, face Mansfield on Saturday.
Israeli PM Benjamin Netanyahu will change his sleeping arrangements on flights after criticism over the cost of installing a special bedroom on a trip to the UK, his office says.
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Energy companies are "overcharging in many cases" with bills failing to fall in line with dropping wholesale costs, the industry's regulator has said.
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Leyton Orient midfielder Michael Collins has signed a new contract which will keep him with the League Two club until the end of the season.