Australia's touring international teams have competed with the logo of Victoria Bitter, a popular locally-brewed beer, on their shirts for a number of years.
Victoria Bitter, known colloquially by its brand "VB", is brewed by Carlton & United Breweries, which was acquired by global brewing giant SABMiller in 2011.
Ahmed, a former Pakistani refugee who received his Australian citizenship in July, made his international debut in the first of two Twenty20 matches against England last week.
He has been named in Australia's squad for six one-day matches that begin in Edinburgh on Tuesday.
Ahmed had requested to be excused from wearing the 'VB' logo as it conflicted with his religious beliefs, Fairfax Media said on Tuesday, and Cricket Australia executive general manager of operations Mike McKenna said the governing body had approved it.
Ahmed is considered a strong prospect for a Test debut when England travel to Australia for their return Ashes series in November. Australia lost the recently completed Ashes 3-0.
South Africa's Muslim batsman Hashim Amla has also been excused from wearing a beer brand logo on his shirts.
Image: Fawad Ahmed
Photograph: Michael Steele/Getty Images
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