The adult male attacked the girl with “a sharp object (not a knife)” near the International English School and the Erikslund school in Borås at around 8.28am on Thursday, the police wrote on their website.
She received minor injuries, consisting of a cut on her arm.
Police have confirmed that the incident is being investigated as a possible hate crime.
“Information has emerged in interviews with the girl that allows it to be classified as a hate crime,” they said in a statement.
According to the teenager, the man said that he attacked her because she was a Muslim.
“He has threatened to kill me, he says that he knows who I am and that he is going to kill me,” she told the SVT broadcaster. “The first time he tried to pull off my veil.”
Around 800 pupils attend the two schools, which kept their doors locked on Friday morning while teaching continued. However, police said that the attack was understood to have been specifically directed at the girl and that they did not believe there was a general threat to the public.
“The police's assessment is that education and other activities can go on as scheduled throughout the day,” police wrote in a statement.
Officers were on Friday afternoon still looking for the suspect, who was described as a man aged around 35-40, 180-190 centimetres tall, dressed in black, with light brown hair and a beard.
The attack took place a day after a 14-year-old boy was attacked with a knife at another school in a different area of Borås. Another teenage boy was arrested as a suspect shortly after the incident.