A silver Ford Focus reversed through the glass front doors at the Smyths toy store, at Kirkstall Bridge Shopping Park, at about 7.20pm yesterday (Sunday).
The shop was closed but staff were working inside at the time of the robbery, police said.
Four men, whose faces were covered, then burst into the shop and threatened one worker with a hammer.
They stole several games consoles and loaded them into the Focus and another car, a silver Volkswagen Golf, which was parked outside, before driving away.
Detective Inspector James Entwistle, of Leeds District CID, said: “This offence was clearly targeted at the games consoles which the store had been stocked with for Christmas.
“It was obviously a frightening experience for the members of staff involved and we are carrying out extensive enquiries to identify the people responsible.
“We would like to hear from anyone who witnessed the incident or who saw either of the vehicles in the area.
“We would also like to hear from anyone who is aware of new games consoles being offered for sale in suspicious circumstances since this incident last night.”
The Focus was carrying the false registration 'YT04EBK', a legitimate plate for a different vehicle, police confirmed.
Meanwhile, the Golf had a partial registration believed to be 'SL06'.
Anyone with information is asked to call Leeds District CID via 101, quoting crime reference 13180579545.
People can also call the independent charity Crimestoppers, anonymously, on 0800 555 111.