"The announcement came without a detailed explanation, leading some commentators to conclude it was retaliation for the Australian Labour Party's (ALP) policy of not selling uranium to India because it is outside the Nuclear Non-Proliferation Treaty," the AAP news agency reported.
But Australia's Department of Foreign Affairs and Trade Secretary Dennis Richardson says that is "flat wrong".
"There is not the slightest suggestion of that by the Indian government," Richardson told a Senate estimates committee, the report said.
Singh's decision to pull out related to domestic issues and the fact that the G20 leaders meeting is scheduled to occur just days after CHOGM, Richardson said.
"Mr Singh wishes to limit time out of his country. "I'm quite confident that Mr Singh's decision does not relate to the issue of uranium."
CHOGM will bring together leaders, delegates and media representatives from up to 54 Commonwealth nations.
Singh's attendance would have been the first visit to Australia by an Indian prime minister in 25 years.
India is now expected to be represented by its vice president Hamid Ansari instead.