Brunei's all-powerful Sultan Hassanal Bolkiah announced last Wednesday that he would push ahead with the sharia law that will eventually include tough penalties such as death by stoning.
Branson said on the weekend that Virgin employees would not stay at the Dorchester Collection luxury hotel chain, which includes The Dorchester in London and the Beverly Hills Hotel in Los Angeles.
"No @Virgin employee, nor our family, will stay at Dorchester Hotels until the Sultan abides by basic human rights," the British billionaire posted on Twitter.
Others who have called for a boycott include comedian Stephen Fry, TV host Sharon Osbourne and comedian Ellen DeGeneres.
The US group Feminist Majority Foundation said it had also pulled its annual Global Women's Rights Awards, co-chaired by Jay and Mavis Leno, from the Beverly Hills Hotel in protest.
The Dorchester Collection is reportedly owned by the Brunei Investment Agency, a sovereign wealth fund under the oil-rich sultanate's Ministry of Finance.
Brunei government officials could not immediately be reached for comment today. The Dorchester Collection also did not immediately respond to a request for comment.
The sultan's move has sparked rare domestic criticism of the fabulously wealthy ruler on the Muslim-majority country's active social media, and international condemnation including from the UN's human rights office.
But the sultan has defended the implementation of the law, meant to shore up Islam and guard the Southeast Asian country against outside influences.
"We have never thought ill of others. We have never relied on them to accept us or agree with is but it is enough if they respect us the way we respect them," he said last week when announcing the law's implementation.
The initial phase introduces fines or jail terms for offences including indecent behaviour, failure to attend Friday prayers and out-of-wedlock pregnancies.
A second phase covering crimes such as theft and robbery is to start later this year, involving more stringent penalties such as severing of limbs and flogging.