Two people in their 30s were injured in the shooting and the condition is critical for one of them, according to the officer in charge of the Greenland police, Jeppe Andsager.
The Greenland police were able to apprehend the man on Saturday morning, after previously urging "citizens in the area to stay indoors, cover their windows and turn off the lights".
The police are investigating the sequence of events, but according to Andsager, the suspected perpetrator was forced to leave a party and then returned with a hunting rifle.
It is possible that two weapons were used, but this is being investigated, he says.
The report of the shooting came in at 7 am local time. Forensic experts from Denmark are expected to arrive in Greenland to assist in the investigation.
Tiniteqilaaq in the Sermersooq municipality had 96 inhabitants according to the 2020 census.