Born in Texcoco, State of Mexico and nicknamed El Emperador ("The Emperor"), Suárez began his club career with UNAM, where he played from 1988 to 1996 where he became champion in 1991. He moved to Guadalajara as an important piece for the 1996 Apertura, and remained there for 3 years, through the 1999 Clausura where he became champion in the Verano 1997 tournament, and was called to the 1998 FIFA World Cup. After being in the All Mexican Team, as an important and solid defender he was transferred to Tigres.
Suárez then moved on to Tigres UANL, where he played from 1999 to the end of 2005. He led the team's defense during that time, and was league runner-up twice, in 2001 and 2003. His last game with Tigres, and in the Mexico league, was a semi-final Clásico Regiomontano in which he was sent off in a controversial referee decision. Previous to this incident, he already had disagreements with the team's management. Tigre's directive organization had asked Suarez to retire for years and join the management, but Suarez had refused. Other differences in defensive style were also cause for conflict with the team's management. The semi-final was the last excuse for separation.
On 8 March 2009, after negotiations with his contract fell, Suarez announced his retirement. However, on 20 March 2009, he decided to return to professional soccer for another year. He was the last active soccer player left from Mexico's 1994 FIFA World Cup squad until he announced his retirement on 26 March 2010.[3]
Suárez was a member and starter for the senior national team in the 1994 FIFA World Cup in the United States as well as the 1998 FIFA World Cup in France. He missed 2002 FIFA World Cup due to injury before the tournament began, but was picked to go to the 2006 FIFA World Cup in Germany. This FIFA World Cup meant his third World Cup in his career. Despite being picked for the squad he saw no action, but he did wear his legendary number 2 jersey.
He captained the national team for many years and officially represented Mexico 177 times (178 in Mexican record keeping) making him the 2nd player with the most caps in history for the Mexico national football team.[5]