The Scottish Defence League (SDL) had planned to lay flowers in Glasgow Green to mark the death of the 15-year-old who was kidnapped, stabbed and set alight by a gang in 2004.
However, the group, which expected up to 50 of its members to attend the event on Saturday, confirmed it would no longer be going ahead after "heated" discussions with police. The SDL has announced it is likely to take legal action after claiming members' human rights are being violated.
The group said it had proposed a series of sites around the Pollokshields area where Mr Donald was abducted. But the organisation said authorities had found issues with all of them and that the SDL may now register as a political party to gain more protection under the law.
Anti-facist campaigners expressed relief at news the SDL event would not be going ahead while Deputy First Minister Nicola Sturgeon accused the group of attemping to hijack the memory of Mr Donald, whose family has previously spoken out against extreme right-wing groups.
Ms Sturgeon, whose Glasgow Southside constituency includes Pollokshields, said: "The SDL's attempted exploitation of the awful murder of Kriss Donald is sickening and is very offensive to local people. The SDL are racists who are not welcome in Pollokshields. They should accept that fact and stop trying to cause disruption once and for all."
Faisal Mushtaq, Zeeshan Shahid and Imran Shahid were sentenced in 2006 to a combined mimimum of 70 years in jail for the murder of Mr Donald, who was targeted because he was white.
Spokesman Graham Walker, an SDL organiser said Police Scotland had told him it may not have resources to protect group members during the planned event and that if it had gone ahead, authorities had strongly indicated that action would be taken against them.
He said: "They're trying to stop us laying flowers. The police have said they can't look out for our safety as Unite Against Fascism will be there and there's a Republican Parade at the same time and if we turn up, we might get orders to move. We feel we are being discriminated against. It's an important part of democracy and freedom of speech to have freedom of assembly. This is the final straw as we've offered numerous different ways for this to take place. We have spoken to our lawyer."
Unite Against Fascism Scotland confirmed that it would have held a counter-demonstration, had the SDL event gone ahead.
Margaret Woods, a spokeswoman for the group, said: "They had originally applied to march through Pollokshields which is one of the most diverse and multi-cultural areas of Glasgow and Scotland. Kriss's mother has said she does not want racists and fascists taking advantage of her son's death. We would have done what we have always done, which is mobilise the community to stand against them peacefully.
"Some of them are fascists. For them to be talking about human rights and all the rest of it is quite ironic and disingenuous."
A Police Scotland spokesman said: "Police are continuing to have dialogue with the Scottish Defence League with a view to minimising the impact any event may have on the local community. Saturday is a busy day in Glasgow with lots of planned events. There will be a strong police presence throughout the city in order to keep people safe."