"This gives a very clear message to athletes that you will be regularly tested to ensure a clean and fair sport," British Bobsleigh's performance director Gary Anderson told the BBC.
"The athlete now has the opportunity to respond to the charge, including the right to a full hearing and testing of their B sample.
"British Bobsleigh will not be making any further comment on the issue until after the full process of investigation has been completed."
If the B sample is positive, the unnamed athlete could be be banned for two years and miss the Sochi winter Olympics.
The British Olympic Assocation is currently awaiting the decision from an appeal by the World Anti-Doping Agency to the Court of Arbitration for Sport against its lifetime Olympic ban for those found guilty of doping offences.