The Crew lost to Cruz Azul 4-0 and 2-0 in group play of the 2009-10 competition but advanced by gaining eight points from its other four games.
The Crew will be at home for the first leg the week of March 9-11 and then travel to Mexico for the second leg March 16-18.
The only MLS team to win its two-leg Concacaf series is Kansas City, which beat Santos in the 2002 quarterfinals. The Wizards then fell 7-2 on aggregate to Morelia in the semifinals.
In other quarterfinal series, Pachuca will face Comunicaciones of Guatemala, Pumas will take on Honduran club Marathon and Cruz Azul will play Panama's Arabe Unido.
The Mexican teams will all host the second legs of their respective series.
2008-09 Concacaf Champions League
Houston Dynamo-Atlante 1-1, 0-3
2007-08 Concacaf Champions Cup
D.C. United-Pachuca 0-2, 2-1
2006-07 Concacaf Champions Cup
D.C. United-Guadalajara 1-1, 1-2
Houston Dynamo-Pachuca 2-0, 2-4
2004-05 Concacaf Champions Cup
D.C. United-UNAM 1-1 0-5
2002-03 Concacaf Champions Cup
Morelia-Columbus Crew 6-0, 0-2
Los Angeles Galaxy-Necaxa 1-4, 1-2
2001-02 Concacaf Champions Cup
San Jose Earthquakes-Pachuca 0-3 1-0
Chicago Fire-Morelia 0-2 2-1
Kansas City Wizards-Santos 1-2 2-0
Kansas City Wizards-Morelia 1-6 1-1