The discovery of widespread fraud in the first round resulted in Karzai losing his more than 50 per cent advantage forcing him into a second round.
The validity of the electoral process and the independence of the IEC have both been called into question.
Abdullah cited the government's refusal to accept his demands for changes in the IEC for his decision to leave Karzai as the sole candidate.
The cancellation of the runoff followed a meeting on Monday between Ban Ki-moon, the UN secretary-general, with Karzai and Abdullah.
Earlier in the day, Karzai had made a plea in an interview with a local radio station calling on Abdullah to reconsider his decision and participate in the runoff, Al Jazeera's James Bays in Kabul reported.
And in an interview with Al Jazeera, Ludin had stressed that the election would be held despite Abdullah's withdrawal.
"Under the law, there is no alternative but to have these elections," our Ludin said.
Bays said that holding the election with one candidate would have posed a "vast organisational headache" and "security headache" even though voters would have been turning out for just one candidate.
The first round of Afghanistan's elections on August 20 was so badly affected by ballot-box stuffing and distorted tallies that more than one million votes were thrown out.
Abdullah had demanded that Karzai sack Ludin and suspend four ministers who campaigned for the president as part of electoral reforms.
He told supporters on Sunday a "transparent election is not possible" and that the Afghan government has been illegitimate since May.
"I'll not take part in the election," Abdullah had said, adding that he had "not taken this decision easily".
In an interview with Al Jazeera shortly after the announcement, he said the decision was made after "a lot of consultations".
"It was the right decision, and I did it in the best interests of this country," Abdullah said.