The break occurred on Wednesday, but the extent of her injury only became apparent on Friday.
Henin is a right-hander who plays with a single-handed backhand, so uses her left hand for nothing more than a ball toss, but the pain was still enough to rule her out for Saturday's opening singles. If she plays at all, Henin might come back for Sunday's doubles.
Henin said the injury was painful but would not have kept her out of a regular tour event. But since Belgium has such strong replacements, there was no need to force her into the singles matches.
U.S. Open champion Kim Clijsters will open the weekend tie against Maret Ani, and Yanina Wickmayer, ranked 12th in the world, will take Henin's place to play Kaia Kanepi in the second singles. Belgium is the overwhelming favorite to advance from the tie into next year's World Group.
Henin should be fit to compete in the WTA event in Stuttgart next week.