On Monday evening, a man was injured by a shot fired through a window in a residential building in the suburb of Kronoparken, east of the centre.
The following night, a second shooting took place in similar circumstances, with multiple shots fired into an apartment which had several people inside. One person was taken to hospital for treatment for gunshot wounds.
A police spokesperson said they were unsure of the extent of the victims' injuries.
Police detained one person suspected of involvement with the shootings on Tuesday and three more on Wednesday evening, as the local newspaper Värmlands Folkblad was first to report.
Local police said they were looking into any possible connection between the two crimes given the similarities, and that they suspected the motive was gang-related.
“We are convinced that this an arrangement within criminal circles. In such cases, it tends to be linked to drugs, weapons and smuggling operations,” police press spokesperson Tommy Lindh told TT.