Namibian President Hage Geingob said in a statement he had accepted the resignations after meeting the two ministers to discuss the allegations, adding they were "innocent until proven guilty".
Citing documents gathered by Wikileaks, The Namibian newspaper, Iceland's national broadcaster RUV and other media reported on Tuesday that the two ministers and the Namibia managing director of South African investment firm Investec had spearheaded a fishing scheme generating kickbacks of at least 150 million Namibian dollars ($10 million) over four years.
Shanghala and Esau did not answer their phones on Wednesday when contacted by Reuters for comment. Investec's Namibian managing director, James Hatuikulipi, could also not be reached for comment.
Investec issued a statement on Twitter saying it had "noted" the media reports. It said it was looking into the matter and would cooperate with the authorities.
Separately, Norwegian bank DNB said on Wednesday it was investigating allegations that Samherji had transferred the bribes via the bank to the Namibian officials.
The Icelandic fishing firm Samherji said in a statement it had hired a law firm to investigate the allegations.
"We have engaged the international law firm Wikborg Rein in Norway to investigate the activities in Namibia. In this investigation, nothing will be excluded and we will disclose its findings as soon as they become available," the firm said.
Samherji said it always acted in accordance with the laws of the countries in which it operated and that it would cooperate with Namibian authorities on the case.
The firm was not available for further comment when contacted by Reuters.
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