Matnadze was introduced to chess at the age of four by her mother. She was trained by Grandmaster Nona Gaprindashvili, amongst others. She won the Georgian Girls' Championship in her age group four times (in 1992, 1993, 1994 and 1998). She won her age group in the Girls' European Youth Chess Championship five times, in Băile Herculane 1994, Verdun 1995, Tallinn 1997, Mureck 1998, and Litochoro 1999.
She won the World Youth Chess Championship twice, becoming the world under-10 girls' champion in Bratislava 1993, and world under-14 girls' champion in Cannes 1997.
Matnadze finished equal second, behind Regina Pokorná in the European Junior Girls CHampionship in Patras 1999, and equal second, behind Jovanka Houska in Avilés 2000. She jointly won the Black Sea Countries Women's Chess Championship in Batumi 2000. Together with Maia Lomineishvili, Matnadze jointly won the Georgian Women's Chess Championship in April 2002. In the same year, she won the European Women's Blitz Chess Championship in Antalya.
She played for the Georgian women's teams NTN Tbilisi and Energy-Investi Sakartvelo in the European Chess Club Cup five times from 2002 to 2006. During that time she won two team gold medals and two individual silver medals (in İzmir 2004 and Saint-Vincent 2005), two team silver medals (in Rethymno 2003 and Fügen 2006), and the team bronze medal in Antalya 2002.
In June 2004, she and WGM Lela Javakhishvili published a letter to FIDE, in which they criticized various aspects of the Women's World Chess Championship 2004, leading to a hostile dispute with FIDE Vice-President Zurab Azmaiparashvili. After initially cancelling her participation, Matnadze was later convinced to play in the event, but was eliminated by Olga Alexandrova in round one.
Matnadze moved to Barcelona and won the Catalan Women's Chess Championship in Balaguer in 2006. She has been the women's champion of the Catalan Chess Circuit in 2008, 2009, 2010, and 2011. She won international tournaments in Mondariz-Balneario 2007, Las Palmas 2009, Tancat Sabadell (Women) 2010, and Benidorm (Women) 2011.
Matnadze became a Woman International Master (WIM) in 1999, a Woman Grandmaste (WGM) in 2002, and an International Master (IM) in 2006.
In March 2012, Matnadze transferred chess federations to represent Spain. She played on board 1 of the Spanish team in the women's division of the 40th Chess Olympiad in Istanbul 2012. She played in the Spanish in the Women's European Team Chess Championship in Warsaw 2013, scoring 6½/9 and winning the silver medal on board 3.
She is a trainer at the chess club Associació d'Escacs Rubinenca in Barcelona, and in the InterAjedrez Academia. She plays in the teams Peona i Peó in Spain, Annemasse in France, Volksbank Halle in the German Bundesliga, and Ankara Demirspor Kulübü in Turkey. She is also involved in other chess activities in Catalonia (Spain).
In 2003, Matnadze graduated from the Tbilisi Ivane Javakhishvili State University, Foreign Language and Literature Department, with a Degree in Philology (German Language and Literature). She knows seven languages, Georgian, Spanish, German, English, Russian, Portuguese, and Catalan.
She received the Grantee of the Foundation of the President of Georgia award in 1998 and 2003, and she was a holder of the scholarship stipend established by the President of Georgia in 2001.
Matnadze is dedicated to the support of international charities. she participated in events such as the chess tournament in Tbilisi to help flood victims in Western Georgia (2005), the charity tournament Chess Against Drugs in Tiblisi (2006), the exchange program Chess and Friendship in Georgia and Spain (2006), the exchange program Chess for peace and understanding in Georgia and Spain (2007), and the chess project We Play For Peace in Las Palmas de Gran Canaria (2009). Since 2005, she has been the President of the International Charity Movement Chess – A Peace Ambassador, a non-profit organisation which has already conducted many international chess and charity events.
Matnadze has a fascination with Vampires and is the main character in a book by Miguel Alvarez Morales, AnnA La Vampiresa (Spanish Edition) (2012, ISBN 4-871-87663-2).
She currently lives in Barcelona, Spain.