The two countries are due to play at Coventry's Ricoh Arena in April, but the world number three will be concentrating on the clay court season by then.
The 25-year-old told Sky Sports News: "It's a shame to miss out on the Davis Cup, as I always enjoy playing.
"I speak to [Great Britain 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."
Smith added: "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."
Britain will be aiming to make the 16-nation World Group playoffs with a win over Russia.