The 25-year-old, who was dropped from the GB team after failing to qualify for Rio, spoke out against technical director Shane Sutton in an interview with the Daily Mail last week.
She alleged Sutton made sexist comments, telling her to "move and get on with having a baby" after her Olympic dream was all but ended.
British Cycling said it was "fully committed to the principles and active promotion of equality".
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"We must take any such allegations seriously," the organisation added, with the review to be conducted in partnership with UK Sport.
Sutton denies any wrongdoing, while Varnish has been invited to meet the equalities officer of British Cycling to discuss the claims.
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