Government agencies have two weeks to review the implications of narrowing the subsidies, he told a news conference.
Malaysia offers subsidies to all citizens, with fuel and cooking oil accounting for the biggest expense. It also subsidises electricity, sugar and flour.
"Subsidies must be targeted, otherwise those subsidies are enjoyed not just by the low income group but also the wealthy," said Anwar, who emerged as leader of the Southeast Asian nation after a closely fought election last week.
Other incentives will be considered for industries that no longer benefit from subsidies, he said.
Anwar is carrying through the stance of the previous administration, which last month proposed a smaller budget, cutting subsidies due to rising commodities costs and the resulting impact on government coffers. Malaysia is estimated to spend a record 77.7 billion ringgit ($17.4 billion) this year on subsidies.
Anwar said he will discuss cabinet appointments with his coalition partners in the next few days.
The 75-year-old was sworn on Thursday, capping a three-decade political journey from protege of veteran leader Mahathir Mohamad to protest leader, prisoner convicted of sodomy and opposition figurehead.
Investors have cheered his appointment, hoping Anwar would bring stability after political uncertainty that saw three prime ministers in as many years.
The focus is on the new government's policy direction and cabinet appointments. Anwar said on Friday he would have a smaller cabinet than those of previous administrations.
($1 = 4.4750 ringgit)
(Reporting by Rozanna Latiff; Writing by A. Ananthalakshmi; Editing by William Mallard)