According to the Daily Star, the duo will instead embark on a second publicity blitz in the hope of raising sales for their new album The Odd Couple.
The group's first album St. Elsewhere went platinum on its 2006 release and included the single 'Crazy', which held the top spot in the UK singles chart for nine weeks.
Despite largely positive reviews, The Odd Couple has so far struggled to match the sales success of its predecessor.
Vodafone TBA's Edinburgh show takes place at the Princes Street Gardens on June 1.