A blue, grey and black-striped blanket the baby had been wrapped in, a red toy dinosaur and a blue baby mirror were in their black Ford Fiesta that was stolen in Dartford on Wednesday, police said.
All the possessions were alongside a blue Stokke iZi Go BeSafe car seat.
The baby's father - who wants to remain anonymous - said: "It's that heartbreak feeling again... It's destroyed me."
He told the Press Association: "I've got his birthday coming up. I can't sleep.  I'm all over the place at the moment, my partner's in absolute pieces.
"They [the thieves] might make a few pounds out of them but it's the memories for us, the sentimental value of it all that no-one can replace."
A Maxi-Cosi car seat and a blue buggy were also in the vehicle, which was stolen from Mead Road.
The buggy had a distinctive leather-coloured handle grip, police said.
Sgt Becky Jones of Kent Police said: "This has caused a great deal of upset and distress for the whole family.
"These items are of huge sentimental value to the victim and the family would desperately like them back."
Kent Police said the Fiesta had a licence plate beginning X389, but it was possible this could have been removed.
The car had recently been undergoing repairs, but still has a faulty bonnet that does not close properly.
Police are appealing for information.
A couple whose baby had recently died have suffered the twin blow of having treasured mementoes stolen.