The match against Russia is due to be played over the first weekend of April, while the second Grand Slam of the year will start on Sunday, May 26.
Despite an almost eight-week gap between the two events, Murray has insisted that his preparations for Paris would be damaged by representing the British outfit.
"I believe I have a chance of winning the French Open, but to do that I need to prepare and use every single day as best as I can," said Murray.
"That's why, unfortunately, I decided not to play Davis Cup this time. I will play the match in September and I'll be available for that.
"I've realised over the years that I play my best when I have time to prepare for each tournament as best as possible. That's why I'm not going to play anything between now and Indian Wells and Miami [in March]."
Murray has never gone beyond the semi-finals at Roland Garos - a feat achieved back in 2011.