The march was due to take place today.
The EDL said it had made the decision out of respect for the grieving family and friends of those murdered by an "ideologically driven individual" in New Zealand.
The shootings on South Island saw 49 people killed and 20 people injured.
A statement from the EDL said: "To give the local Muslim community and other people time to reflect on these tragic events we suspended our planned demonstration. We reiterate that we abhor what has happened in New Zealand and condemn those who have perpetuated this pain and suffering on innocent people.
"The EDL committee will convene and set another date for our return to Wellington."
Police in Wellington were left with hundreds of pre-packed lunches due to the march being suspended.
They have been given to sheltered schemes across Telford.
The English Defence League (EDL) demonstration is no longer taking place in Wellington today.— Wellington SNTs 🚔 (@WellingtonCops) March 16, 2019
But West Mercia Police @TelfordPatrol have been left with hundreds of pre-packed lunches which we are now distributing along with @TWStreetPastors to sheltered schemes across Telford pic.twitter.com/iHBtkeiZdv