A 21-year-old woman has been arrested after injuring three people in a knife attack at a further education college in Warsaw, the third assault on a school in Poland in less than a week.

The suspect used a "dangerous object" at around 12:30pm local time (10:30 GMT) on Saturday to attack a 17-year-old woman at the institution, said Jakub Filipiak, a spokesman for Warsaw police. Two other people, aged 17 and 24, were also injured in the incident.

"One person was injured and transported to the hospital with non-life-threatening injuries. Two other bystanders also sustained injuries but did not require hospitalisation," Filipiak said.

Police did not identify the educational institution but confirmed it was open on Saturday because it is a higher education establishment. National media identified it as TEB Edukacja, a post-secondary school where the suspect was enrolled. Police said the attacker did not know any of the victims.

The attack came hours after Polish police announced they had detained 76 people across the country and checked nearly 50,000 schools nationwide as part of efforts to prevent further violence following two earlier incidents.

On Wednesday, a 19-year-old student attacked fellow students, teachers and passersby with a sharp object at a vocational school in the central Mazovian province, injuring nine people before being arrested nearby.

The following day, a 15-year-old killed a school custodian and wounded two others in a knife attack at his former primary school in Leszczydol-Nowiny, north of Warsaw, in the same province.

Both attacks were carried out by Polish nationals and shocked a country where school violence by minors is described as a new phenomenon.

By Thursday night, rumours that the attacks were coordinated and that further violence was planned for a so-called "bloody Friday" were circulating in parents' online groups and in mainstream media. Fifty-nine schools pre-emptively suspended classes on Friday, the majority in the Mazovian district.

School directors sent messages announcing stepped-up security measures, including extra staff at entrances and voluntary backpack checks. Many parents kept children at home.

Interior Minister Marcin Kierwinski also said a 17-year-old was detained in the town of Sierpc, north-west of Warsaw, after allegedly stating on school grounds that he planned to harm someone.

"There will be no compromise here. The safety of the youth is the most important thing," Kierwinski said.

Prime Minister Donald Tusk also addressed the situation ahead of the nationwide police operation. "When it comes to the safety of Polish children and peace in our schools, there is no room for compromise," he said.

A Warsaw police spokesperson said authorities could not confirm whether Saturday's attack was related to the two previous incidents. The government said it had found no evidence that an internet challenge promoting school attacks was ongoing, though local media, citing a police spokesperson, reported that authorities had information suggesting the incidents this past week could be related to such a challenge. There is no official confirmation that any of the attacks are linked.