The raid happened at around 1.30am yesterday morning (April 28) when the masked suspects drove into the forecourt of the Jet petrol station in Leagrave High Street.
One of the men got out of the minibus, attached a chain to the cash machine and used the bus to rip the machine open before taking the cash from inside and driving off.
Both he and the driver were wearing face coverings.
The minibus is believed to have been stolen from Bedford Square, Houghton Regis, by suspects in blue gloves and hoodies just after 1am the same morning.
PC Glenn McAlpine-Given, investigating, said: “These criminals are clearly dangerous and need to be taken off the streets.
“If anyone saw anything or has any footage which can help our enquiries, whether from Luton, Houghton Regis or somewhere in between, please get in touch with us.
“Whether it’s dash cam, CCTV, doorbell footage – if you have any information that can help our investigation, we would really appreciate your support.”
Anyone with any information can contact police online or call 101 quoting reference 40/23726/22.
Alternatively you can give information via Crimestoppers, anonymously, on 0800 555 111 or online.