The interior ministry, which supported a bill in parliament putting forward the measure, said live broadcasts of attacks in other parts of the world had unwittingly revealed police positions and other tactical details.
Prime Minister Lee Hsien Loong has said an attack on the wealthy island, home to thousands of multinational corporations, is not a matter of if but when.
Fears have been heightened by support for the Islamic State (IS) group in Muslim-majority neighbours of the financial hub. In 2016 police foiled a plot to fire a rocket at Singapore from an Indonesian island.
It also bans the sending of text and audio messages about security operations and authorises police to take down or disable any drones in the area, regardless of their intention.
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The ministry said the proposed new powers were necessary as the city-state "continues to face a clear and present security threat" from self-radicalised individuals at home and from "foreign terrorists who view Singapore as a prized target".
Singapore is one of the world's most wired countries, with high ownership of mobile devices and fast internet speeds.
Those who contravene a police order to stop communicating could face up to two years in jail or a fine of up to Sg$20,000 (USD15,000), the Straits Times newspaper reported.