The announcement comes amid an investigation into lead presenter Jeremy Clarkson’s suspension following a “fracas” with a producer on the show.
The BBC said new dates for all four performances will be announced within a fortnight. There were no plans at present to postpone any other live dates.
Clarkson has been suspended since 10 March following allegations that he punched producer Oisin Tymon.
BBC Director General Tony Hall is expected to receive a report on the incident next week.
Meanwhile, Clarkson has said comments criticising the BBC he made at a charity event in London were meant as a joke.
The presenter was filmed giving an expletive-laden description of the corporation’s bosses at an event on Thursday.
An online petition for the Top Gear host to be reinstated has so far received more than one million signatures.
Top Gear is one of the BBC’s most popular and profitable TV shows, with an estimated global audience of 350 million.
Its success is largely attributed to the Clarkson, who has appeared on the show since 1988.
Last May the presenter was given what he called his “final warning” by bosses at the BBC after claims he used a racist word during filming.
The BBC said that he and his co-presenters James May and Richard Hammond had been due to renegotiate their contracts with the BBC next month.
The group have separate contracts to promote Top Gear across the world with the BBC’s commercial arm, BBC Worldwide, which are reported to expire in September.