A woman in her twenties, who was passing when the explosion occurred in the centre of the city Lund around 2.30 am (0030 GMT), was found injured at the scene and taken to hospital.
Police Evelina Olsson told AFP she had “serious but not life-threatening injuries”. The blast was believed to be intentional.
“We have reports that windows as far as 100 metres away have been damaged,” Olsson said, adding that they had started an investigation for “causing bodily injury” and “destruction causing public endangerment”.
No arrests had been made by noon Saturday but police had been in contact with the owners of the small convenience store which was the apparent target.
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Criminal use of explosives has been increasing in Sweden with 120 cases reported in the first six months of 2019 compared to 83 in the same period last year, according to statistics published by newspaper Dagens Nyheter.
On Saturday, Sweden's Minister for Home Affairs Mikael Damberg said the government wanted to introduce harsher sentences for smuggling and possession of explosive substances.
About 90,000 people live in Lund, near Malmo.
It is also the seat of Lund University, one of the oldest and largest universities in Sweden, with 40,000 students.
See a map below to see the explosions in the nearby city of Malmö so far this year.