The 21-year-old, whose hits include "Run It!" and "Kiss Kiss," was sentenced in August 2009 to five years probation, ordered to perform 180 days of community service and attend domestic abuse counselling.
The tour was due to have started in Glasgow on Wednesday, followed by gigs in Birmingham, Manchester and London on Thursday, Friday and Sunday respectively.
It was postponed "due to unforeseen circumstances," according to the website promoting the tour. Fans were advised to hold on to their tickets with the possibility of the dates being re-arranged.
The Home Office said: "We reserve the right to refuse entry to the UK to anyone guilty of a serious criminal offence. Public safety is one of our primary concerns. Each application to enter the UK is considered on its individual merits."
Brown has the right to appeal.
(Reporting by Mike Collett-White, editing by Paul Casciato)
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