In a statement released on Thursday, organisers said that the decision to postpone was taken following a meeting with officials and partner agencies.
They said it is currently not safe to hold the event, and with a “heavy heart” were left with no choice but to postpone.
The event – one of the UK’s largest indoor music festivals – was due to be held at the Royal Highland Centre, Ingliston on October 30 and 31.
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The decision to cancel was taken as it was deemed to be a higher risk than any other event currently scheduled to go ahead in Scotland.
The statement said: “We fully understand that this will come as a major disappointment to our loyal 40,000 ticket holders planning their trip to Edinburgh for Halloween weekend.
“With festivals and events now happening up and down the country, this decision is particularly hard to bear, but we must stay strong and hold on another five months for what will be the biggest, most incredible Terminal V to date.”
All tickets for this month’s event will automatically be transferred to the new Easter, 2022 date.
An announcement is expected later today on a smaller event which has been permitted to run at the Edinburgh O2 Academy the weekend of November 12, with priority tickets set to be available for Terminal V ticket holders.