The shots were fired at a 25-year-old man on an open street near Möllevång Square on Sunday evening, and the boy was arrested just a few minutes after the police were alerted.
Sunday night, another 25-year-old man was shot in connection with an apartment in the Hermodsdal district. His condition is also reported to be serious but stable.
We see no connection between these events at present. There are two completely separate investigations being conducted, says police spokesperson Nils Norling.
Initially, there is no apparent connection to the shootings and explosions in Copenhagen recently.
It's something we'll also look into in both cases, says Norling.
No one has been arrested for the shooting in Hermodsdal, and it is still unclear whether one or more perpetrators were involved.
On Monday afternoon, senior prosecutor Caroline Carlqvist reports that the arrested 13-year-old has not yet been questioned by the police.
Due to his young age, the police investigation cannot lead to a prosecution.
In cases like this, when it comes to very serious crimes, one can consider bringing a civil lawsuit in the end, says the prosecutor.
In that case, a trial will be held to determine whether the boy is guilty.
But it cannot result in any punishment, as social services are involved in a situation like this, says Caroline Carlqvist.
At present, the police have not arrested any suspected client of the shooting.
Corrected: In an earlier version, the wrong street name was given for the incident on Möllevången.