Police believe that the female was a random victim of the shooting while the male may have ties to local gangs, North Zealand Police said.
The woman has been released from hospital while the man is still at Copenhagen's Rigshospitalet in stabile condition.
The tabloid Ekstra Bladet reported that people connected to the biker gang Satudarah were spotted at the hospital after the man was admitted.
The shooting took place at around 7pm outside of the Sticks N' Sushi restaurant in the department store, which is located on the main street of Lyngby, a northern suburb of Copenhagen. The area was packed with shoppers at the time, police said.
“It was a special day with a lot of sales in the area. We take this very seriously and are investigating it from there,” North Zealand Police spokesman Henrik Suhr told broadcaster DR.
As of Monday morning, no suspect had been apprehended but police were looking for a man thought to be around 30 years old who might be connected to the incident. Police are also searching for a white car seen leaving the area with three men inside.
A gun was found in the shopping centre but police said that it has not yet been confirmed that it was the weapon used in the shooting.
“We have investigated throughout most of the night and now we need to put things together,” Suhr told DR early on Wednesday.