Asad Shah, 40, died after being found with serious injuries outside his shop in the Scottish city of Glasgow on Thursday evening.
He was believed to be a member of the minority Ahmadi community, and media reports said he was originally from Pakistan.
Police arrested a 32-year-old Muslim man on Friday, and a spokeswoman said: “A full investigation is underway to establish the full circumstances surrounding the death which is being treated as religiously prejudiced.”
In a statement on Saturday, the Ahmadiyya Muslim Community UK condemned the “completely brutal, horrific and unjustified attack”.
The day before his death, Shah had apparently posted a message on Facebook reading: “Good Friday and very happy Easter, especially to my beloved Christian nation x!”
Scottish First Minister Nicola Sturgeon joined a vigil for Shah outside his shop on Friday night, while locals gathered again on Saturday to pay tribute to a man they said was a pillar of the community.