A number of armed police were despatched to the school in the town of Ishøj near Copenhagen after the student, who was previously expelled from the school, reportedly made the threats.
Ambulances as well as armed police were seen at the school, local media sn.dk reports.
Police confirmed via Twitter shortly after the incident that a man had been arrested.
He was expelled on Monday and consequently made the alleged threat against the Next Gymnasium upper secondary school, where the incident took place.
The threats have been taken seriously by police and the man is expected to appear in court on Tuesday with a view to being remanded in custody over the offence, West Copenhagen Police have confirmed.
The alert was raised at around 1pm on Monday with the arrest taking place around two hours later.
Gymnasium is the Danish term referring to a three-year upper secondary school education programme which qualifies students for admission to university.