The head of BHP's petroleu
m division Mike Yeager will also not be paid any extra for the past financial year after the massive impairment charge on the assets bought in 2011.
The company also cut the value of its Australian nickel division by US$450 million, with the price of the commodity down and costs rising.
Plunging US gas prices forced the global giant to book a writedown on the value of the Fayetteville shale gas assets in Arkansas that it acquired from Chesapeake Energy.
But it did not write down its other shale liquid and gas assets in Texas and Louisiana acquired through Petrohawk Energy, also last year.
It comes after British energy giant BP was hit by a huge impairment charge on its US shale gas assets.
Kloppers, who was reportedly paid more than US$15 million last year, said it also reflected BHP's decision to adjust its development plans by shifting drilling from dry gas to more liquid-rich fields.
"While we have responded appropriately to the changed market conditions today's impairment is clearly disappointing," he said, adding that he believes the assets will still prove their worth in the longer-term.
"We believe that our dry gas assets are well positioned for the future given their competitive position on the industry cost curve."
Shale gas is produced by tapping gas from shale rock using a technique called hydraulic fracturing, or "fracking".
Little-known even five years ago, natural gas trapped in sedimentary shale rock is seen as having the potential to transform global energy markets.
BHP chairman Jac Nasser welcomed Kloppers' and Yeager's decision to forgo any bonus as the company's share price dropped more than two percent to Aus$31.31 by early afternoon, near three-year lows.
"As a result of the writedown both Marius Kloppers and Mike Yeager have advised the remuneration committee that they do not wish to be considered for a bonus for the 2012 financial year," he said.
"The remuneration committee and the board respect and agree with that decision." Nasser added that the writedown demonstrated the company was operating in "difficult times", but threw his support behind Kloppers.
"We are fortunate to have Marius' leadership, together with a strong management team supporting him, in these challenging times," he said.
"Notwithstanding the prevailing environment we are confident in the outlook for the United States natural gas market and the role our shale assets will play in BHP Billiton's portfolio in continuing to deliver long-term shareholder returns."