The man lives in the first-floor apartment in which the fire was started, said duty officer Stig Heidemann of East Jutland Police.
"The reason we suspect that he is behind the fire is that he behaved strangely when we arrived at the scene. He wanted to go back into the apartment and almost began hitting officers so he could get in. That is not normal," Heidemann said.
"We know a bit about him already. Not because of arson, but for small inconsequential things," the officer added.
The fire was reported to police at 1:37am.
When police and fire services arrived at the location, they found several bottles lying on the ground outside.
"Some of the bottles had contained flammable liquids," Heidemann said.
28 people were evacuated from the building. Nobody was injured.
"It could have ended very badly. Luckily, most people were able to get out, and we had to go around waking quite a few," the duty officer said.
The residents were temporarily accommodated at a nearby retirement home on Wednesday morning.
"We are in the process of finding out who can go back into their apartments and who can't," Heidemann said.
Five to six apartments are too damaged by the fire for residents to return to them, police and fire service sources said.
The 27-year-old is expected to be brought for a preliminary hearing Wednesday on arson charges.