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.
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.