The performer received a suspended sentence following a trial that sparked international debate.
Wednesday's gig alongside Swedish rap artists Jireel, Z.E and Dree Low is set for Stockholm's Ericsson Globe, a golf ball-shaped arena that is the world's largest spherical building.
A$AP Rocky's booking agency Live Nation said part of the concert's proceeds would go to charity.
The 31-year-old rapper will have to be on good behaviour during his stay in Sweden to avoid seeing his suspended sentence change to a spell behind bars.
A$AP Rocky, whose real name is Rakim Mayers, was arrested on July 3rd a few days after a brawl in Stockholm in which he and his entourage were embroiled with a 19-year-old plaintiff. Considered a flight risk, he was held in custody for a month while the case was investigated and throughout his trial.
Prosecutors had called for a six-month prison sentence, but the court said the actions of Mayers and two members of his entourage were not severe enough to warrant more time in prison. The court did not specify the length of the suspended sentence.
Assault carries a maximum penalty of two years in prison in Sweden.
Mayers' imprisonment outraged fans, who started an online petition, #JusticeForRocky, which garnered more than 640,000 signatures. Supporters were urged to boycott Swedish brands such as Ikea.
The case also led to diplomatic tensions after US President Donald Trump
himself called for Mayers to be released.