Australian Weightlifting Federation chief Michael Keelan has levelled the accusation at Daniel Koum and said he and other team members had been forced to dig into their pockets before the weightlifter would compete.
Cameroon-born Koum said he was "very disappointed" at the allegations.
"I'm very shocked," he told Australian Associated Press. "I've always been competing. I've put all my financial money to represent this country and they're accusing me of (asking for) $5,000?
"With past competitions, even I just went to represent Australia in the world championships and it cost me more than $10,000."
Keelan said the incident occurred at the Oceania championships in Samoa last week, which doubled as an Olympic qualifier and where the Australian men's team needed a good finish to win a place in London.
Concerned that Koum was not sufficiently motivated to reach his potential in his competition, Keelan offered him a $1,000 incentive, the official told ABC radio.
"You think that everyone who's representing Australia does so with pride and with commitment and, unfortunately, we heard that wasn't the case with Daniel Koum," Keelan said.
"So I personally thought, well, the best way to negate any negatives out of all this would be to, by offering, sort of, some money, whereby he could actually compete and have some incentive to do the total that we asked of him...
"But then later on, it changed from an agreement to actual demand and he said that he would not lift unless he got $5,000, before he started the warm up for his own event.
"And then it was pretty frantic... we had to find that money. And say, within about 30 minutes we handed over the $5,000."
Koum came to Australia to compete at the 2006 Commonwealth Games for Cameroon before becoming a citizen and competing for his adopted country at the 2010 Commonwealths in Delhi.
The Australian Olympic Committee said it had spoken to the AWF and was launching an investigation into the incident.
"The AOC is working with the Australian Weightlifting Federation (AWF) to investigate the matter," read a statement.
"The AOC investigation will be ongoing."
Koum could conceivably yet represent Australia at the London Games after the AWF nominates its single male entry to the AOC this weekend, although he conceded that was now unlikely.
Keelan said he had no regrets about offering the incentive.
"(I felt) sick in the guts," Keelan recalled. "I was under duress. We had to make a call very, very quickly. And, you know, the call was that we would submit to his demand."