The Star newspaper quoted national police chief Khalid Abu Bakar as saying the 13 Malaysians were arrested in a raid on a restaurant in a Kuala Lumpur suburb.
He added they bring the number of people arrested since April this year over suspected IS links to 36.
“We are constantly monitoring these kinds of activities. Militancy and terrorism have no place in this country,” he was quoted saying.
The story gave no further details on the nature of the alleged IS links. Khalid and other senior police officials could not immediately be reached for comment.
Authorities have previously confirmed at least 30 to 40 Malaysians had already joined the bloody civil war in Syria, and that IS supporters were actively seeking more recruits via social media.
Officials fear recruits will become radicalised and bring back violent extremist views.
The story did not say whether the 13 arrested had planned to travel to Syria.
In August, Malaysian police said they foiled a plot for a wave of bombings drawn up by radical Islamic militants inspired by the Islamic State group.
More than a dozen people arrested from April to June were formulating plans to bomb pubs, discos and a Malaysian brewery of Danish beer producer Carlsberg, police said, adding that some had planned to travel to Syria first.
Local media have previously reported that 26-year-old Malaysian factory worker Ahmad Tarmimi Maliki killed 25 elite Iraqi soldiers in a suicide car-bomb attack there in May.
Malaysia has previously been home to several suspected key figures in groups such as al-Qaeda-linked Jemaah Islamiyah, a Southeast Asia-based organisation blamed for the deadly 2002 Bali bombings and numerous other attacks.
But the activities of such regionally based groups have been greatly diminished by counter-terror actions over the years. – AFP