The king resigned on Sunday after just two years on the throne, the first time a monarch has stepped down before completing their five-year tenure.
No reason was given for the resignation.
Malaysia is a constitutional monarchy and the king assumes a largely ceremonial role, including acting as custodian of Islam in the Muslim-majority country. The king's assent is needed for the appointment of a prime minister and various senior officials.
Malaysia's nine royal households take turns to provide a king, who is chosen through a vote in a Council of Rulers, made up of the nine households, most of which are led by a sultan.
Heads of six of the nine households met on Monday at the national palace to decide a date for the election of a new king, Bernama reported. It was not clear why the other three did not attend.
A vote must be held within four weeks of the throne becoming vacant.
King Muhammad, 49, had resumed duties last week after spending two months on medical leave,
Images purporting to show him getting married in Russia appeared on social media in December and identified his new wife as Oksana Voevodina, who won a Miss Moscow contest in 2015.
The palace did not respond to earlier requests for comment on the photos or reports of a marriage.
Media has reported tension between the palace and the government of Prime Minister Mahathir Mohamad since the latter returned to power last year.
Mahathir led the opposition to a historic election win in May, defeating a coalition that had governed Malaysia for 60 years.
In June, the government and palace faced a near two-week impasse over a plan to appoint someone how was not from the majority ethnic Malay community as attorney-general.
The king eventually approved the appointment, though the incident had stoked ethnic tensions.
Mahathir, known for challenging royalty during his earlier 22-year tenure as prime minister, said in a blog post last week that everyone "from the Rulers to the Prime Minister and Ministers, to the civil servants and ordinary citizens" are subject to the law. He did not elaborate.
Mahathir said on Monday the government hoped the council would elect a new king as soon as possible as the government needed to keep the king apprised on "certain matters", Bernama reported.