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Police were called to the scene at Brunnsparken in the western Swedish city shortly after 12.30pm, reports local newspaper Göteborgs-Posten.
The girl, who was reportedly bleeding from her stomach, was taken to hospital by ambulance. At 2pm her condition was described as “serious but stable”.
Her age was not immediately known, but she was described by police as “a young girl” and witnesses described her as around ten.
A migrant in his mid-30s was seized by police immediately after the incident. There were no other suspects.
The girl’s grandmother, in her mid-60s, was injured while trying to prevent the attack, but her injuries were not serious.
The man was caught after youths who were passing by wrestled him to the ground. Security guards and an off-duty police officer also helped, according to the police.