The minister for equalities, sport and leisure has not specified when she will attend the Games, which take place in February, but her intent to travel to Sochi has been confirmed.
Prominent politicians from across the world have announced their intention to boycott the sporting fixture.
A spokesman from gay rights charity Stonewall, said they did not support people staying away.
But he said there are other ways to make a point such as a country sending less important politicians.
Ruth Hunt, deputy chief executive of Stonewall, added: “We have worked closely with Russian lesbian, gay, bisexual and transgender activists who have been clear they don’t support a boycott of the Winter Olympic Games.
“Instead, we need to make sure that the British Government and campaigners continue to raise awareness of the situation in Russia and stand with activists for the long haul.”
American president Barack Obama is following in a similar vein by sending openly gay former tennis player Billie Jean-King and Caitlin Cahow, a former ice hockey international, in his absence.
Alex Heah, a former winter Olympics competitor
France’s president Francois Hollande, plus Joachim Gauck, president of Germany and Canadian prime minister Stephen Harper, have also announced they will not be attending.
Neither will EU Commissioner Viviane Reding.
In June Russian president Vladimir Putin signed into a law a ban on “propaganda of nontraditional sexual relations.”
It was justified as being an attempt to promote traditional Russian values over western liberalism and means fines can be imposed on people who provide information about the lesbian, gay, bisexual and transgender community to under 18s.
The International Olympic Committee has clarified that athletes competing in Sochi are free to speak out against Russia’s new law as long as they do so in designated protest zones.
Several attempts were made to contact Helen Grant directly but we were unable to get a response.