In a televised address on Tuesday, Muhyiddin said the parliament will be suspended for a stipulated period of time, and that elections would not be held during the emergency, which could last until August 1.
"Let me assure you, the civilian government will continue to function. The emergency proclaimed by the king is not a military coup and curfew will not be enforced," Muhyiddin said, in an attempt to dispel alarm over the measures.
Some lawmakers in the ruling coalition have pulled support for the premier and have called for early elections, while opposition leader Anwar Ibrahim said last year that he had a majority to form a new government.
Muhyiddin assured people that elections would take place once a new independent committee declares that the pandemic is over and it is safe to hold polls.
Under emergency rule, his government can introduce laws without parliamentary approval.
On Monday, Muhyiddin announced a nationwide travel ban and a 14-day lockdown in the capital Kuala Lumpur and five states, saying the healthcare system for the country of 32 million people was at a breaking point.
The number of new daily infections hit a record high last week, breaching the 3,000 mark for the first time. Total coronavirus cases passed 138,000 on Monday, with 555 deaths.
Malaysia's benchmark share index fell as much as 1.6% after the emergency announcement.
'Critical stage'
Malaysia's palace said Muhyiddin requested King Al-Sultan Abdullah to declare a state of emergency as a proactive measure to curb Covid-19.
The declaration will last until August 1 or earlier, depending on whether coronavirus infections have been brought under control, it said.
"Al-Sultan Abdullah is of the opinion that the spread of Covid-19 is at a critical stage and that there is a need to declare a proclamation of emergency," the palace said in a statement.
The king had rejected a similar request from Muhyiddin in October. Opposition leaders had then criticized the request as a move to cling to power.
Malaysia is a constitutional monarchy in which the king has a largely ceremonial role, carrying his duties with advice from the prime minister and cabinet. But, the monarch also has the power to decide if an emergency should be declared, based on threats to security, economy or public order.
Nik Ahmad Kamal Nik Mahmood, legal expert at the International Islamic University of Malaysia, said the government will gain wide powers during the emergency.
"The constitution is more or less suspended, as a substantial part of it can be overridden by emergency law," he said.