Rocky was filmed involved in a street altercation which he says was an act of self defence. Following the incident he went to the police to explain the situation, and was arrested along with two other men.
Daniel Suneson of the City Public Prosecution Office said he came to the conclusion that a crime was committed after "studying the videos made available to the inquiry".
He added: "It is worth noting that I have had access to a greater amount of material than that which has previously been available on the internet."
A petition calling for his freedom has now reached close to 630,000 signatures, and US politicians and Kanye West are among those throwing their support behind the calls.
Last week Donald Trump spoke to Swedish Prime Minister Stefan Löfven and said he received assurances “that American citizen A$AP Rocky will be treated fairly”.
A$AP Rocky will remain in custody until trial, and no trial date has currently been set.
Patrick Hinton is Mixmag's Digital Features Editor, follow him on Twitter
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