The fire happened just before 1 a.m. Tuesday.
Police say two people were evacuated from separate apartments. Officers were told four people lived in four apartments in the building. A third resident was staying at a friend's house, but the fourth tenant could not be found in the house.
Authorities say that resident approached officers to turn himself in just before 3 a.m.
WAOW-TV reports the suspect was booked into jail. A bail hearing is scheduled Wednesday.
No one was hurt. Fire officials say the building was destroyed.