Michael Savage and his wife Mel had travelled to a friend's house in Loughton, Essex, from West Bridgford in Nottinghamshire, during the wet and windy conditions on Monday.
Due to the poor weather, they ran inside and left lots of Christmas presents and the urn containing the ashes in their BMW, Essex Police said.
Mr Savage, 29, said his wife's father "travels with us to all significant family gatherings so that he can share in the occasion".
"We just leapt in the house as the wind was howling. We know we shouldn't have left the presents and the ashes in the car, but we just wanted a hot drink and some rest after battling down the motorway for over three hours.
"We are staying with our close friends over Christmas and then travelling to my parents' home on Boxing Day so we brought down with us a boot full of Christmas presents.
"We are just sorry to all our friends' children who will have to wait several more weeks for some new presents.
"My father-in-law's ashes reside with us in our Nottinghamshire home, but he travels with us to all significant family gatherings so that he can share in the occasion.
"If anything, we appeal to the thieves to contact the police with the location of the ashes so that we can have Mel's dad back with us."
Essex Police said the car was stolen between 11pm on Monday and 10am yesterday from outside a house on Lower Park Road.
The black BMW 118d has a registration of PY08 NZW.
A police spokesman said: "We're desperately looking to find this man's car and his wife's father's ashes as well as the thieves who stole it.
"With this in mind, sightings of this car or anyone who saw people acting suspiciously near the junction of Lower Park Road and High Road in Loughton overnight should contact us."
Anyone who knows of the whereabouts of this car is urged to contact Essex Police on 101.