The venue, on the border between Shropshire and Staffordshire, usually hosts the car show around this time every year, but organisers said concerns over coronavirus means they will delay until later this year or next year.
All existing bookings for the show, which was due to take place on April 12 and 13, will automatically be transferred to the rescheduled event.
Organisers Classic Shows said: "Our number one priority is the welfare and safety of our staff, visitors, traders, exhibitors and venues.
"It has already been necessary to cancel our next two events due to take place at Three Counties Showground, Malvern and Weston Park, near Telford. We have not currently cancelled any further events and are continuing to assess the position in light of ongoing Government advice. As such we will continue to make further announcements about the remaining schedule of events over the coming weeks.
"We hope that you and your families stay safe and hope to see you all before long."