Tsonga, 28, dominated the quarter-final matchup winning 7-5, 6-3, 6-3 before a partisan crowd at Roland Garros.
Federer, appearing in the 36th Grand Slam quarter-finals of his career, struggled to deal with Tsonga’s blistering serve, clocked at well over 200 kilometres an hour, and made uncharacteristic mistakes that played to the Frenchman’s advantage.
The 31-year-old Swiss earlier struggled to reach the quarterfinals, after losing the first two sets against Frenchman Gilles Simon before battling back to win the round in five sets.
Any sense that he was going to repeat that feat against Tsonga, ranked number nine in the world, was shattered in the third set.
Tsonga made a number of remarkable recovery shots, while Federer, ranked number three in the world, missed serves and a couple of overhead volleys.
The winner of 17 Grand Slams will now look to Wimbledon and the US Open to salvage the year.
Switzerland's other great hope at Roland Garros, Stanislas Wawrinka, faces a tough challenge on Wednesday against defending French Open champion Rafael Nadal.