Police said security at a hospital was stepped up after the gunfire was reported, adding that "one person had been taken to hospital in a private car".
Feuds between criminal gangs fighting over territory have taken place in major Swedish cities in recent years.
Aftonbladet said the shootings were next to a police station so officers were there immediately.
There were no immediate details on the conditions of the injured men.
Pictures from the scene of the shooting show armed officers as well as a large number of paramedics.
Malmo is in the southwest of Sweden and is the port of entry for those crossing the Oresund Bridge from Denmark.
- AP