The Midlands venue for the Europe/Africa Zone Group I second round tie from April 5-7 was confirmed on Thursday with the winners to compete in the World Group play-offs in September.
But Britain's hopes of progressing have been badly hit with the absence of the world number three.
Murray said: “It's a shame to miss out on the Davis Cup, as I always enjoy playing. I speak to (GB captain) Leon (Smith) and the team on a regular basis and will definitely be available to play the next Davis Cup tie later this year.”
The Scot, who did not played for Britain in either of their 2012 ties, will play in the Masters events in Miami and Indian Wells in March and then take a break before commencing his European clay court campaign in Monte Carlo from April 16.
Smith, who will now be forced to call upon the likes of Jamie Baker, Josh Goodall and James Ward - all ranked outside the world's top 200 in singles, showed empathy.
He said: “We are very excited to be taking Davis Cup to Coventry and taking advantage of strong home support. It will be tough against Russia, who are arguably the strongest team in our group, but we'll be giving it our best shot.
“We totally understand Andy’s position. He has worked extremely hard on his game elevating it to another level and we have all seen the fruits of that since Wimbledon.
"Andy’s success continues to inspire more and more young people to take up the sport and we look forward to welcoming him back into the team in September.”
Great Britain secured promotion to Group I during their 2011 campaign and received an opening round bye in this year's competition.