The company, viewed as the most experienced bidder, announced its withdrawal on Friday, confirming a Dec. 14 Reuters report that cited a spokesman for Rio 2016.
Aggreko said in a statement that as it had not been awarded the first tranche of contracts, which had been broken into different segments, it had pulled out of bidding for the rest.
The British firm has been involved in nine Olympics as well as six soccer World Cups, and its withdrawal is a worrying sign for Rio organisers who are under huge pressure to cut spending as Brazil languishes in its worst recession in 25 years.
The government has already warned there is no money to cover any cost overruns.
Some analysts have said the withdrawal may also hit Aggreko's 2016 earnings. The company had already warned in August that markets were likely to remain difficult next year, after a profit warning in July.
For the 2012 Olympic Games in London, Aggreko's power deal was worth nearly $60 million, although the Rio 2016 contract was expected to be worth less as it is smaller in scope.
"It won't impact earnings expectations but it does support our view that Aggreko has lost some of its sparkle in recent years," said Stifel analyst Caroline de Soujeole, who has a "sell" rating on the stock.
Aggreko shares, down 37 percent so far this year, were up 0.7 percent at 907 pence by 0805 GMT.
The temporary power contract is a vital part of Olympic preparations, guaranteeing a stable and secure energy supply for international broadcasters, the opening and closing ceremonies, as well as back-up electricity for the venues.
Two sources with knowledge of the tender told Reuters earlier this week that the companies left in the running were a mix of Brazilian and international firms, but that it was unlikely any of them had the in-country capacity and Olympic experience to fully meet the needs of the contract.
It is likely that whoever wins would have to lease generators from Aggreko, they said.
(Editing by Mark Potter)
By Li-mei Hoang