Emergency medical services deputy superintendent Mike Bosse said all of the patients' symptoms were minor, and all were aged between 16 and 25.
He blamed alcohol and drug use for the problems, but some concert-goers blamed oppressive heat inside the TD Garden arena.
A spokeswoman for concert promoter Live Nation said early reports indicate that a majority of the 36 people taken to hospital were people outside who were too intoxicated to be allowed into the venue.
Avicii, whose real name is Tim Bergling, called the medical issues "awful news" on his Twitter account. "Its a terrible thing, I rly hope everyone is ok! My thoughts go to those affected & their families." (sic)
The incident came after two people died over the weekend at a Las Vegas music festival attended by Avicii, one of the biggest names in electronic dance music. Authorities said on Monday that it will take several weeks to determine what caused the deaths of the Electric Daisy Carnival fans.
Police said nearly 800 people were treated for medical conditions and 25 were hospitalised during the three-night electronic music festival, which organisers said drew about 400,000 people at the Las Vegas Motor Speedway.
Festival organisers told police that 134,000 fans attended Friday, Saturday and Sunday night shows featuring pulsing lights, Ferris wheels, seven stages of music and DJs including Avicii, Diplo, Afrojack and Tiesto.