According to newspaper 20 Minuten, the couple were due to travel by train on an Interregio service heading for Biel/Bienne on Tuesday.
After boarding the train at Lyss in the canton of Bern with their weeks-old baby in a pram, they realized they hadn't validated their tickets.
The pair left the train to punch their tickets and it was at that point that the doors shut and the train moved off.
Contacted by 20 Minuten, a train conductor who was on duty that day confirmed that he found an unaccompanied baby on the train after being alerted by passengers.
A spokesman for Swiss federal railways (SBB) told the paper: “It's true that we find all sorts of curious things on trains, like army-issue guns or wheelchairs. But to my knowledge it's the first time that we're found a stroller with a baby.”
The child's parents quickly reported what happened to rail station staff and were reunited with their baby in Biel/Bienne.
According to the paper, the baby slept throughout the journey.