Fabbri was born in Rufino, a small city in Santa Fe, where he grew up playing in the same age group as Guillermo Coria, also a native of Rufino.

Turning professional in 2001, he reached a career high singles ranking of 328 in the world, which he attained in 2004.

[1] He made his only ATP Tour main draw in 2007 at the Croatia Open Umag, partnering Carlos Berlocq to the quarter-finals of the doubles.

His biggest title win was also in doubles, at the 2008 Asunción Challenger.

Since retiring from professional tennis he has worked as a tennis coach and in 2021 he joined the coaching team of Diego Schwartzman, assisting Juan Ignacio Chela.