He went on medical leave in November and, the following month, photographs emerged that appeared to show him marrying a former Miss Moscow in the Russian capital.
While the position is largely ceremonial, the monarch is tasked with upholding Malay and Islamic tradition.
A statement from the national palace confirmed the resignation of the relatively youthful monarch, known for his fondness for four-wheel driving and other extreme sports.
The statement added: "His Highness has worked towards fulfilling his responsibilities entrusted to him as the head of state, serving as a pillar of stability, source of justice, the core of unity. for the people".
Speculation intensified about the king's future after his medical leave officially finished at the end of December, and the country's Islamic royals reportedly held a special meeting last week.More news: Lady Gaga, 'Roma' shine at nice over nasty Golden Globes
Sultan Muhammad V's decision marks the first time a king has abdicated in the Muslim-majority country since it gained independence from Britain in 1957.
No reason has been given for Sultan Muhammad V's resignation, which takes effect immediately.
The Malaysian government hopes that the country's new king will be selected as soon as possible, Prime Minister Mahathir Mohamad said on Monday (Jan 7).
The couple Wednesday in Moscow at a lavish ceremony following strict Islamic traditions, including being alcohol free with halal food.
"When Mahathir was asked to confirm the marriage in November, he said he "[did not] have any official confirmation, so I can't say anything".More news: China's central bank to pump US$210 billion into ailing economy
Muhammad V was just 47 when he became king, and has garnered a reputation for having relatively youthful interests. It follows weeks of speculation that the ruler would step down.
Mohd Amar Nik Abdullah, the deputy chief minister of Muhammad V's seat of Kelantan, said Thursday that his administration had not heard anything and urged country's attorney general to "take action" against those spreading rumours.
According to the rotation in place, the Sultan of Pahang would be next in line.
"There is no constitutional crisis, it is an internal issue that is resolved by the royal rites".More news: Rami Malek confirms romance with Bohemian Rhapsody co-star Lucy Boynton