Dzagnidze has played for the Georgian national team in the Women's Chess Olympiad, the Women's World Team Chess Championship and the Women's European Team Chess Championship. Her team won the gold medal at Dresden in 2008; she scored scoring a 7/10 points. In 2014, at the Women's Chess Olympiad in Tromsø, Norway, Dzanidze won the individual gold medal as the best player on board one, ahead of Hou Yifan. In the Women's World Team Championship, she won the team bronze medal in 2011 and 2017. In the Women's European Team Championship, Georgia won the silver medal in 2005, 2009 and 2017. Dzagnidze an individual board four gold medal in 2007.