The 27-year-old will be replaced in the quadruple sculls, which starts on the opening day of the Games on Saturday, by Jack Beaumont whose father Peter competed in the 1988 Seoul regatta.
"Seven years of dedication and it's all over before getting to take a stroke in anger," said Thomas, who has won world championship silver and bronze medals, in a team statement on Tuesday.
"I don't agree with the decision but I don't think anyone in my shoes would, as an athlete you always back yourself."
Britain has never won a medal in the quad sculls since the event was introduced in 1976.
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The team said Thomas, a former rugby union player and key member of the squad over the past three years, had probably incubated the virus before arrival.
The rower paid tribute to his parents, who had travelled to Rio to watch him, and vowed to bounce back and plan for the next Games in Tokyo.
Beaumont won a World Cup silver medal with the men’s quadruple scullers in Lucerne in May when he was also drafted in as a substitute.
"Whilst we welcome Jack into the team and we know that he is a quality substitute with a proven medal record, it is nonetheless a decision that we have taken with heavy heart because Graeme has worked so hard to be here and has been such a strong part of the crew," said rowing team leader David Tanner.
(Reporting by Alan Baldwin, editing by Toby Davis)
