In the doubles, Andy's brother Jamie, ranked fifth in the world, will partner doubles specialist Dominic Inglot.
"This date is a real nightmare for everybody, not just for him (Andy Murray), because it's not easy to change surface again," Smith told reporters.
"I was hopeful last week that he would play but then he goes and wins Wimbledon and has Olympics and U.S. Open coming up and I hope he does well there also. As a team we are all delighted for him.
"I hope he comes out Thursday or Friday to support the team."
World number 73 Daniel Evans, who was named in the initial squad, also missed out due to personal issues and a shoulder injury.
Murray has committed to playing at the 2016 Rio Olympics, where he will look to defend his title.
The quarter-finals will take place between July 15-17 at the Tasmajdan Stadium in Belgrade.
(Reporting by Nivedita Shankar in Bengaluru; editing by Sudipto Ganguly)
