A 21-year-old woman and her 24-year-old husband were caught by police in Meidling train station transporting the cocaine and a small amount of heroin under the baby.
The ORF reported that both the suspects were the child's parents, although other media reports only confirm the woman was the mother.
Police say they had been observing the station in Vienna after receiving a tip off that a large amount of narcotics was going to arrive at one of the city's train stations this week.
The drugs were being transported in pellets and had a street value of around €150,000 according to police.
Both suspects were taken to Josefstadt prison and the baby is staying with the mother.
The male suspect said he had nothing to do with the further sale of the drugs and told police he had been given the nickname of someone to hand them over to.
It is not clear from where the couple had travelled nor where the drugs came from.