The assembly law replaces legislation that required a police permit for public gatherings, but critics complain it contains a range of new restrictions including an outright ban on street marches.
Prime Minister Najib Razak had framed the law as part of a campaign to soften tough rules on security, free speech and assembly as he looks to increase support ahead of elections expected next year.
Najib has defended the legislation, saying it guarantees the right to peaceful assembly.
The law allows gatherings to be held in designated places, such as stadiums, without prior notice, while those in other areas would first require police approval.
The law was softened slightly in the wake of the outcry, shortening the amount of notice that assembly organisers must give police to within 10 days of the event, instead of the original 30 days.
But critics including the Bar Council and Amnesty International maintain the act would grant police too much power over the timing, duration, and location of gatherings.