"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," Clooney wrote on website Deadline Hollywood.
"I've learned over years of dealing with murderous regimes that you can't shame them. But you can shame the banks, the financiers and the institutions that do business with them and choose to look the other way," he added.
The nine hotels are located in the US, Britain, France and Italy.
Brunei will implement the harsh new penal code -- which also mandates amputation of a hand and foot for theft -- starting next Wednesday.
Homosexuality is already illegal in the tiny sultanate, but it will now become a capital offence. The law only applies to Muslims.
Brunei first announced the measures in 2013, but implementation has been delayed as officials worked out the practical details and in the teeth of opposition by rights groups.
In addition to film-making chops that have netted him two Oscars, Clooney is known for his globe-trotting political activism, especially his tireless campaigning to draw attention to the conflict in Sudan's Darfur region.