Local media, citing unnamed sources, said Law's relatives were taken away from their homes in Hong Kong for questioning, then released.
The Hong Kong police said in a statement that they "took away two men and a woman for investigation" from the island of Lantau on suspicion of assisting persons wanted by the police for activities that endangered national security.
Law declined to comment when contacted by Reuters.
Law is among eight overseas-based activists who were issued with arrest warrants last week by the Hong Kong police for alleged offences under a national security law that China imposed in Hong Kong in 2020.
This was the first time that relatives of an activist have been questioned after the issuance of the warrants and a bounty of HK$1 million ($128,000) for information leading to any arrests.
Some rights groups criticised the police move.
"It is sinister that the Hong Kong authorities questioned the family members of Nathan Law," said Mark Sabah, with the Committee for Freedom in Hong Kong Foundation.
"This tactic mirrors how the Chinese government targets the families of Uyghurs, Tibetans and other dissidents abroad. This latest escalation is clearly designed to intimidate and silence Hong Kongers abroad."
Hong Kong's pro-Beijing leader John Lee has said that the eight activists should be treated like "street rats" that people should avoid or report on.
Law publicly severed ties with his family in Hong Kong in August 2020, and was granted political asylum in Britain two years ago.
Last week, police arrested five former members of the disbanded political group Demosisto, for running an online commercial platform that was allegedly used to provide financial aid to Law, according to local media and sources.
They were later granted bail, according to a source with direct knowledge of the matter.
Demosisto was founded by Law and other activists, but disbanded after the enactment of the national security law.
The security legislation has been criticised as a tool of repression by governments including the United States, but Beijing says it has restored stability to Hong Kong after protracted pro-democracy demonstrations in 2019.
(Additional reporting by Hong Kong newsroom; Editing by Christina Fincher and Alex Richardson)
By Jessie Pang and James Pomfret
