Labadze had a successful junior career, notably reaching the final of the Wimbledon boys' singles in 1998 and losing to future World No.1 Roger Federer. Together with Lovro Zovko he won the 1999 French Open boys' doubles.

Labadze's most successful appearance at a Grand Slam event came at the 2006 Wimbledon Championships, where he reached the fourth round. After eliminating Gastón Gaudio and Mardy Fish, he was defeated by the eventual runner-up Rafael Nadal in three sets. It was to be his last appearance in the singles main draw at a major championship. Labadze's best result in Masters 1000 tournaments was reaching the semifinals of the 2004 Indian Wells Masters. After defeating Carlos Moyá and James Blake, he lost to Tim Henman in straight sets.