The bill was proposed after a string of attacks in Kenya by Somalia-based Shebab insurgents that have increased pressure on the government to confront the Islamist militants.
Divisions over the bill led to a heated debate culminating in punches being thrown, forcing the vote to be delayed until 1700 IST, according to a local journalist in parliament.
Earlier in the day an opposition lawmaker yanked a copy of the legislation from a majority MP's hands and tore it into pieces.
Under the bill, journalists could face up to three years behind bars if their reports "undermine investigations or security operations relating to terrorism," or if they publish images of terror victims without permission from the police.
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"This is a serious assault on the freedoms that Kenyans are enjoying today. We believe that the amendments are just a way of sugarcoating the bill," said opposition coalition leader Moses Wetangula, referring to minor changes made to the proposal.
"It is important that the legislation, while strengthening security, respects human rights and international obligations," they said. "Protecting Kenya's constitution and upholding civil liberties and democracy are among the most effective ways to bolster security."
Newspapers also said that while action to increase security needed to be taken, some of the proposals were too severe.
"The very real and present dangers must not be used as an excuse to roll back the gains of a free and democratic society," the Daily Nation's editorial read.
"There is nothing to fear about the Bill unless you have been engaging in criminal activities," Uhuru said.
As part of an ongoing security crackdown prompted by the attacks, Kenya on Tuesday closed over 500 non-governmental organisations, including 15 for alleged fundraising for terrorism.