The 49-year-old king's resignation on Sunday took effect immediately, the National Palace said in a statement. No reason was given and palace officials did not respond to requests for comment.
Malaysia is a constitutional monarchy and the king assumes a largely ceremonial role, including as the custodian of Islam in the Muslim-majority country. However, the king's assent is needed before the appointment of a prime minister or senior public officials.
The country has nine royal households, who typically take turns to sit on the throne, and the selection of the next king is decided by a vote in the Council of Rulers, made up of all nine royal households.
Heads of six of the households met on Monday at the national palace to decide a date for the election of a new king, national news agency 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 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.
