Born in Montevideo, Canobbio started playing professionally with C.A. Progreso (2000–04), going on to represent in his homeland Deportivo Colonia (2005–06) and C.A. Rentistas (2006). For the following four years he competed abroad, with Spain's AD Cerro de Reyes (2007), CD Onda (2007), CD Buñol (2008) and CD Olímpic de Xàtiva (2009–10) and Greece's Makedonikos FC (2008–09), always in lower league football.
In 2011, Canobbio returned to his country and Progreso, freshly returned to the Primera División.
Canobbio's older brother, Fabián, is also a footballer. A midfielder, he also played in Spain but with much more success, notably winning La Liga and the UEFA Cup with Valencia CF; they shared teams at Progreso.
- "El Olímpic ficha al central uruguayo Carlos Canobbio" [Olímpic signs Uruguayan centre-back Carlos Canobbio] (in Spanish). Las Provincias. 4 March 2009. Retrieved 22 February 2012.
- "Los hermanos Canobbio hicieron líder provisional al Progreso en Uruguay" [The Canobbio brothers made Progreso the provisional leader in Uruguay] (in Spanish). Qué!. 1 September 2012. Retrieved 21 June 2016.