Police said a bin was placed at the rear door of a house in the Westbourne Street area and set alight in the early hours of Tuesday morning.
The couple managed to get the baby – who is just weeks old – out of the property unhurt.
The fire caused substantial damage to the bin and the rear door.
Alliance councillor Maire Hendron has condemned the attack.
“The people inside the house were very lucky that the fire did not spread to the house, otherwise we could have been looking at a tragedy today,” she said.
“We should also be thankful that the parents were able to get their baby out of the house before it was able to inhale any smoke which would have been very serious for such a young baby.”
She described the actions of the perpetrators as “extremely reckless” and added: “The people responsible for this attack obviously have no regards for the lives of other people.”
East Belfast MLA Michael Copeland said the arson attack has “shocked” the local community.
“Such reckless behaviour could easily have led to a much graver situation.”
The Ulster Unionist politician said: “I am sure that this experience has been extremely upsetting for the family, especially when they had their baby in the house.”
Police are investigating the incident and have asked anyone with information to come forward.
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