Rutherford's partner Susie Verrill, who will not attend the Games with their young son, said the couple had taken the precaution because they wanted to have more children.
"The Zika news has caused no end of concern," she wrote in the Standard Issue magazine.
"We'd love to have more children and, with research in its infancy, I wouldn't want to put myself in a situation which could have been prevented.
"We're not ones to worry unnecessarily, but after more than 100 medical experts stressed the Games should be moved to prevent the disease from spreading, this was a huge factor in us choosing to stay put."
Athletes from the British triathlon team have also been prevented from going outdoors after dusk, because of fears of the virus.
"If you stand outside at dusk, mosquitoes will start congregating so we are not doing that. We will be indoors," performance director Brendan Purcell told British media.
U.S. cyclist Tejay Van Garderen withdrew from the Games last week, over concerns that the outbreak could present risks for his pregnant wife.
(Reporting by Nivedita Shankar in Bengaluru; Editing by John O'Brien)
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