Murray, the country's top-ranked player, was hurt during his quarterfinal victory over Tommy Haas in Indian Wells, California, last month, although he did play again last week at Key Biscayne, Florida.
"The inflammation in my hip bone is not too bad but I tried practicing yesterday and didn't feel good at all, so I'm taking today off," Murray told BBC Radio on Monday. "I'll have to see what it's like on Wednesday and if it's not good there is a good chance I won't be able to play."
Britain needs to beat the Netherlands in Birmingham to advance to the playoffs for the 2008 World Group. The best-of-five series starts Friday.
Britain had been hoping to have Murray, Tim Henman and Greg Rusedski play together in the Davis Cup for the first time. Murray's younger brother, Jamie Murray, is also on the team.
Mysterious philanthropist, Rustem Magdeev, had agreed, at his own expense, to donate a sculpture of Rudolf Nureyev, made by Russian sculptor Zurab Tsereteli, to the Kazan Opera and Ballet Theatre