Communication Workers' Union members were set to walk out at 11am on 19 October in a protest over pay, pensions and jobs.
Last week, the CWU notified Royal Mail of its intention to strike for the first time since the 501-year-old firm was privatised in 2013.
Royal Mail on Monday applied to the High Court for an injunction to prevent any strike action before an agreed mediation process for settling labour disputes had been exhausted.
A Royal Mail spokesman said strikes would now not be possible until the Christmas period at the earliest.
The ballot is part of a flurry of union activity this autumn as public sector and health workers discuss the possibility of industrial action.
Royal Mail responded to the announcement by calling the action "illegal".
Royal Mail confirms that the High Court has today ruled that the contractual dispute resolution procedures under the Agenda for Growth must be followed before industrial action can take place.
'The mediation process will take close to Christmas to be completed, and may be longer.
CWU general secretary Dave Ward said last week that the dispute was a "watershed" moment that would determine not only members' pensions, jobs and pay but also the future of the UK's postal service.
"Postal Workers" attitude towards the company will harden and it makes us more determined than ever. The company claimed that under an agreement with the union the CWU must enter mediation with Royal Mail before embarking on industrial action.
'We will now make contact with the union as a matter of urgency to begin the process of external mediation. We want to use them to do just that.
'We are very committed to working closely with the union in order to reach agreement as a matter of priority'.
Speaking outside the court, Mr Ward said there was now a timeframe for a round of external mediation, adding: "We believe that still means we can take action before Christmas".