His career began in his hometown with Awasa Tbilisi. Moving to play for Metalurg Rustavi, Dinamo Tbilisi and Alania Vladikavkaz he was transferred to SC Freiburg in 1998, where he was one of several Georgians in the squad. In his first half season with Freiburg, he helped the club earn promotion to the Bundesliga. The club managed to avoid relegation the following season, and in 2001 even qualified for the UEFA Cup, finishing fifth in the league. The following season, however, Freiburg were relegated back the second division. After earning promotion to the Bundesliga a second time, in 2003, Kobiashvili transferred to FC Schalke. With Schalke, he finished second in the Bundesliga twice, in 2005 and in 2007, and played in the final of the DFB-Pokal in 2005. In 2005–06, he helped Schalke reach the semi-finals of the UEFA Cup, which Schalke lost to the eventual champions FC Sevilla. In 2008, he reached the quarterfinals of the UEFA Champions League, which Schalke lost to FC Barcelona. Over six and a half years with Schalke, Kobiashvili made his way into Schalke's international record books. Having played thirty five international club matches, he ranks third among Schalke players, and is tied for fourth with Klaus Fischer, Kevin Kurányi, and Licoln on goals scored in international competitions, with seven.
On 20 December 2009 he announced he would be leaving FC Schalke 04 to transfer to Hertha BSC. He joined his new club on 1 January 2010.
During a relegation playoff game against 2. Bundesliga team Fortuna Düsseldorf, Kobiashvili punched referee Wolfgang Stark after the final whistle. Hertha lost the playoff 4–3 on aggregate goals and was relegated from the Bundesliga as a result. Kobiashvili was banned for one year, retroactively beginning 16 May 2012. The German Football Association later reduced Kobiashvili's suspension for seven and a half months, to end 31 December 2012.