The call came as a growing list of politicians and celebrities added their names to those condemning the new laws and supporting a boycott.
"I commend my friend, #GeorgeClooney, for taking a stand against the anti-gay discrimination and bigotry taking place in the nation of #Brunei - a place where gay people are brutalised, or worse - by boycotting the Sultan's hotels," the singer wrote on his Twitter page late last Saturday (March 30).
The 72-year-old, a veteran gay rights campaigner, said his "heart went out" to staff at the hotels, but that "we must send a message, however we can, that such treatment is unacceptable".
The nine hotels mentioned by Clooney are located in Britain, France, Italy and the United States. They include London's exclusive Dorchester and the Beverly Hills Hotel in Los Angeles.
The Dorchester Collection luxury chain issued a statement saying that its code emphasises "equality, respect and integrity in all areas" and that "we do not tolerate any form of discrimination", CNN reported.
Clooney called for the boycott earlier this week, saying "every single time we stay at or take meetings at or dine at any of these nine hotels, we are putting money directly into the pockets of men who choose to stone and whip to death their own citizens for being gay or accused of adultery".
"No one should face the death penalty because of who they love. Brunei's decision is barbaric," Britain's international development minister Penny Mordaunt wrote on Twitter.
Former New Zealand prime minister Helen Clark called the new penal code "shocking" and "barbaric".
Amnesty International called on Brunei to "immediately halt its plans to implement these vicious punishments".
In the US, Clooney's call drew supportive declarations from lawmakers on both sides of the political aisle and a strong statement from the Trump administration.
"We strongly oppose human rights violations and abuses against LGBTI persons, including violence," the State Department said in a statement.
LGBTI stands for Lesbian, Gay, Bisexual, Transgender and Intersex. Intersex people are people born with physical features that are neither wholly male nor female.
Former US vice-president Joe Biden, who is expected to seek the Democratic Party's 2020 presidential nomination, tweeted last Friday: "Stoning people to death for homosexuality or adultery is appalling and immoral.
"There is no excuse - not culture, not tradition - for this kind of hate and inhumanity."
Another Democrat seeking the party's nomination, Senator Kamala Harris of California, joined the chorus. "These human rights abuses cannot be tolerated," she said.
And Senator Ted Cruz, a Republican from Texas, said on Twitter: "This is wrong. It is barbaric. America should condemn this immoral and inhumane law, and everyone should be united against it."
Actress Jamie Lee Curtis also tweeted in support of her fellow actor's stand. "I stand with George Clooney, a good man doing the right thing, fighting an unjust and barbaric law."
Clooney and his wife, human-rights lawyer Amal Clooney, have been active in humanitarian causes.
Brunei, an absolute monarchy ruled for 51 years by Sultan Hassanal Bolkiah, is to implement the new penal code starting on Wednesday.
Homosexuality is already illegal in the sultanate, but it will now become a capital offence. The law applies only to Muslims.
Brunei first announced the measures in 2013, but implementation had been delayed in the face of opposition by rights groups, and as officials worked out the practical details.