He brandished the weapon at the toddler  while demanding a handbag from the child's mother on Albion Grove, Sale, at about 09:15 GMT on Friday.
The man ran on to Roebuck Lane towards the canal towpath, and stole money before dropping the bag.
The mother and child were "unharmed but distressed".
The man is described as white with a tan, slim, in his mid to late 20s, about 5ft 8in, (1.73m) with green eyes and was wearing a baggy dark grey hooded top and grey trousers.
Det Insp Helen Bell from Greater Manchester Police said: "Luckily no one was hurt in this terrifying robbery, but the victim has suffered significant psychological distress as a result.
"To threaten a baby with a gun is utterly reprehensible, I cannot imagine how awful an experience this must have been for both the woman and her child.
"We are taking this very seriously and we currently have officers in the area tracing where the man was before the incident and where he went after."
Anyone with information is asked to contact police or Crimestoppers.
Police are hunting a "reprehensible" robber who pointed a gun at a three-year-old child.