"The arrest was made with the help of the National Task Force and Gothenburg's police force," she said.
The National Task Force (Nationella insatsstyrkan) is the Swedish police's special operations unit.
Sweden's terror alert level has been at an 'elevated' level for a year, but Kvarnström reports that incidents in Gothenburg haven't raised the alert level further.
"There's an ongoing judgment made, and it can always be changed. But right now we've judged that there is no reason to take security-raising measures in Swedish society in general," Kvarnström told TT.
"There's no cause for the general public to be concerned," she said.
Sara Kvarnström doesn't want to comment further on the events of the night.
The arrest occurred during the night between Saturday and Sunday, near Röda Stens Konsthall, an art gallery by the Älvsborg Bridge.
Gothenburg's International Biennial for Contemporary Art's opening party was ongoing at the gallery, when the police arrived on the scene.
Just after midnight, the police asked the gallery's manager to evacuate the area.
"I don't know much more than that the police threw us out, and said they'd arrested four people suspected of terror crimes. Then they cordoned off the whole area," said manager Mia Christersdotter Norman to daily newspaper Expressen.
Gothenburg police confirmed that an area around Röda Sten has been cordoned off.
On Sunday morning, the police website informed the public that the area was evacuated and cordoned off because of "a threat that implied serious danger to lives, health or extensive property damage."
"I can't say anything else, because we aren't giving any information from here," said Gunilla Gustafsson, of the police's county communications centre, to TT.
Röda Sten now shows no sign of last night's evacuation. Photographer Adam Ihse, from Scanpix photo agency, was at the spot earlier Sunday morning.
"There's nothing left, no cars, no policemen. It looks exactly like normal," said Ihse to TT.
The arrest was made ten years to the day since the terror attacks in New York.