The rare machines, worth hundreds of thousands of pounds, were taken by thieves who targeted a vintage store in Weybridge, Surrey.
Other gaming machines were also stolen in the burglary on The Games Room, in Hamm Moor Lane.
Collectors have been asked to help look out for the stolen items.
The machines are "extremely distinctive" and have unique serial numbers, making them easily recognisable, police said.
The burglary happened between 17:00 BST on 28 August and 08:00 the next day, but details have only just been released by Surrey Police.
PC Matt Ladd said: "Our enquiries so far have led us to believe that this was a thoroughly researched and pre-planned job.
"We are very keen to speak to anybody who saw anything or who has heard conversations around this incident."
He urged anyone who saw pictures of the items on sites like eBay or Gumtree, or who knew of someone selling them at car boot sales or vintage fairs, to get in touch.
A first edition Beatles jukebox worth more than £20,000 is among vintage items stolen in a "pre-planned raid", said police.