The Southeast Asian country has already secured 12.8 million doses from its deal with Pfizer-BioNTech signed last month, as well as from its participation in the global COVAX facility, backed by the World Health Organization (WHO).
"This means that we have secured vaccine supplies to cover 40% (of the population)," Muhyiddin said in a televised address.
Malaysia expects to buy enough supplies to inoculate 26.5 million people, or more than 80% of its people.
The government is now in final negotiations with China-based manufacturers Sinovac and CanSino as well as Russia's Gamaleya Institute to cover the remainder, Muhyiddin said.
The procurement deals are expected to cost MYR2.04 billion (US$504.4 million) in total, he said.
In order to boost confidence in the safety and efficacy of the vaccines, Muhyiddin said he would be among the first to receive a dose, followed by frontliners and high-risk groups such as senior citizens.
The government expects to receive the first batch of the Pfizer-BioNTech vaccine in February, he added. Malaysia was the first country in Southeast Asia to strike a deal with the US drugmaker.
Under the Pfizer deal, it will receive 1 million doses in the first quarter of 2021 and 1.7 million, 5.8 million and 4.3 million doses in the subsequent quarters.
Neighbouring Singapore was the first Asian nation to take delivery of the Pfizer vaccine on Monday when its first batch arrived from Belgium.
