The Star wrote that the Dane was arrested alongside a British man and a Kenyan woman. The arrest took place in the upscale Nairobi neighbourhood of Gigiri, one of the largest expat communities in Africa.
The trio was arrested by a team of special investigators and then turned over to Kenya's Anti-Terror Police Unit, The Star wrote.
The al-Shabaab jihadist group is officially designated as a terrorist organization by the United State, the United Kingdom, Australia, Canada and the United Arab Emirates.
The group is mostly affiliated with al-Qaeda but a faction of al-Shabaab has pledged allegiance to Isis. The jihadists are perhaps best known for a 2013 attack on the Westgate shopping mall in Nairobi in which 71 people, including the four attackers, were killed.
The group has also claimed credit for several attacks in Somalia, including a restaurant bombing as recently as October 1st that killed two people. Just a few days later, al-Shabaab militants killed six Christians in the northern Kenyan town of Mandera in one of many attacks to explicitly target non-Muslims in the area.