It will be the second successive home tie played at the All England Club after Britain defeated Croatia 4-1 at the same stage last September in Tim Henman's final tie.
That victory put John Lloyd's side into the World Group, but a 4-1 first-round loss to Argentina in February means they must win another play-off to get back into the elite group.
Lloyd said: "I am delighted that this crucial tie is going to be played at Wimbledon, which is a fantastic venue and I firmly believe that playing on grass will give us the best opportunity to win the tie.
"It's a tough draw but one that we are fully capable of winning. I am sure tennis fans will get behind the team and come along to support the players in our bid to return to the World Group in 2009."