Flammable liquid was poured through the letterbox of a house on Ormeau Embankment about 06:20 BST on Saturday but details have only just been released by police.
Damage was caused to the inside and outside of the front door.
Police have appealed for anyone with any information to contact them.
A woman in her 30s and three children have escaped injury but been left shocked after an arson attack in south Belfast.