There is one muslim student organisation at the University of Tromsø - Muslim Academia Tromsø, and you will find their web-site here. You can contact the leader: Asad Akhter 98193858
There is a Muslim prayer room at the University campus in Breiviklia. For many muslims it's normal to pray salah five times a day, and the Mosalla is provided so that Muslim students and employees can practise their salah in a dignified way.
The Mosalla, at University Campus are located - with its own enterance - at the north end of the Breiviklia-building (see map). You can recieve the code to the door from Asad Akhter 98193858 or University Chaplaincy. Phone or mail.