Rurik Jutting was held after police found the victims in an apartment in the Wan Chai area. They were called there at 03:42 on Saturday (19:42 GMT).
One woman, aged between 25 and 30, was found with stab wounds, and the body of a second woman was found inside a suitcase on the balcony.
Local reports said the women were believed to be sex workers.
Hong Kong Police said they had detained the man and retrieved a knife from the apartment in the J Residence block ,which is situated in an affluent area and is reportedly popular with professional people working in the financial sector.
Assistant district commander Wan Siu-hung told reporters that the woman whose body was in the suitcase had been dead "for quite some time" and had neck injuries.
Speaking about the other dead woman - who had stab wounds to her neck and buttocks - he said: "We believe the death was caused by a sharp object which cut the throat of the deceased.
"When police found her she was lying in the living room - the room was messy."
The two women are believed to be of Asian or South East Asian origin.
The South China Morning Post reported that police had found a small amount of cocaine in the apartment and that they were examining the arrested man's mobile phone.
The suspect was a former employee of Bank of America Merrill Lynch, local reports also suggested.
A resident of the 40-storey block, who said his fellow occupants were mainly expats, told the newspaper: "It was a shock because you would never expect something like this to happen in Hong Kong."
A spokesperson for the UK Foreign Office said: "We can confirm that a British national has been arrested in Hong Kong.
"We are in touch with the local police and stand ready to provide consular assistance."
Post-mortem examinations are being conducted to determine the causes of the women's deaths.
Historically Hong Kong has enjoyed a relatively low crime rate. According to the Hong Kong Police website, there have been 14 homicides between January and July, down from 56 over the same time period in 2013.
A 29-year-old British man has been arrested on suspicion of murder after the deaths of two women in Hong Kong.