The news follows a fight on the street in Stockholm last Sunday.
The rapper was due to be headlining Wireless festival in London this Sunday, 7 July, but will remain in custody in Stockholm while an investigation takes place.
Wireless hasn’t yet responded to Newsbeat’s request for comment.
ASAP Rocky, real name Rakim Mayers, was arrested earlier this week following his appearance at Smash festival in Stockholm.
A video published online appears to show him punching another man in the street.
Swedish authorities had until Saturday to decide whether to formally take action and, following a detention hearing in Stockholm, Sweden’s Prosecution Authority decided he will remain in custody.
If the investigation isn’t concluded in two weeks’ time, they can apply to keep ASAP Rocky for another two weeks.
His charge has been reduced from aggravated assault to assault.
Another person arrested with ASAP Rocky on suspicion of aggravated assault has also been detained, while one more is still waiting for their hearing. The third, his bodyguard, who was arrested on suspicion of assault, was released earlier this week.
In videos posted to ASAP Rocky’s Instagram, he and the people he’s with repeatedly tell a pair of men to stop following them.
One of the men accuses the 30-year-old’s team of breaking his headphones.
In the caption for the first video ASAP Rocky writes: “We don’t know these guys and we didn’t want trouble. They followed us for four blocks.”
In the second, he accuses the man of hitting his security guard “in the face with headphones”.
As well as Wireless on Sunday, ASAP Rocky was due to perform at Longitude in Ireland on Friday.
He’s already missed out on Open’er Festival in Poland, where he was scheduled to headline on Thursday, with Stormzy stepping in to replace him.
Newsbeat has contacted ASAP Rocky’s team for comment.