The law took effect on Monday and sets guidelines for the manner in which customs are allowed to carry out digital searches, according to Radio NZ.
Under the updated law, officials would need to have reasonable suspicion to ask a traveller to provide access to a digital device - whether through a password, pin, fingerprint or face recognition.
Anyone who is asked to provide access and refuses, faces a fine and seizure of the device in question.
Brown claimed the law was a "delicate balance" between the right to privacy and the duties of law enforcement.
Thomas Beagle, a spokesman for the New Zealand Council for Civil Liberties, criticised the law and described it as an invasion of privacy that was not required.
"Nowadays we've got everything on our phones; we've got all our personal life, all our doctors' records, our emails, absolutely everything on it, and customs can take that and keep it," he said.
Beagle added that any serious criminals would avoid carrying incriminating material on devices and store it online. "You'd be mad to carry stuff over on your phone," he said.
A total of 540 electronic devices were searched at airports in the country in 2017.