Twitter said it had suspended all information requests from Hong Kong authorities immediately after the law went into effect last week.
Facebook and its messaging service WhatsApp said on Monday they are suspending requests from the Hong Kong government and law enforcement authorities for information on users.
The pause will take place "pending further assessment" of a new national security law imposed on Hong Kong by China, and would include "formal human rights due diligence and consultations with human rights experts", a Facebook company spokesman said in a statement.
"We believe freedom of expression is a fundamental human right and support the right of people to express themselves without fear for their safety or other repercussions," the spokesman said.
WhatsApp might not survive in the country
China last week enacted the sweeping security law for the restive city of around 7.5 million people, banning acts of subversion, secession, terrorism and collusion with foreign forces.
The legislation, which has sent a wave of fear through the territory, has criminalised dissenting opinions such as calls for independence or autonomy.
Digital rights group ProPrivacy called Facebook's move "a win for both digital privacy and human rights in the region."
"With the stakes so high, and the punishments so severe, it is great news to see big tech companies like WhatsApp pushing back in favour of democracy and freedom of expression," the group said.
However it noted the move could lead to WhatsApp being blocked in Hong Kong as it has been in mainland China.