Juan Monaco is scheduled to open the best-of-five series against the Czech Republic's Tomas Berdych before del Potro goes against Ivo Minar.
Both the Czech Republic and Argentina are missing usual Davis Cup single players because of injury. Argentina's Davis Nalbandian is recovering from hip surgery and Czech Radek Stepanek is bothered with a knee problem. However, Stepanek is expected to try to play doubles.
The matches in Ostrava are set for a hard court indoors.
After the singles matches Friday, a doubles match pitting Argentines del Potro and Leonard Mayer against Stepanek and Lukas Dlouhy is scheduled. Berdych faces del Potro, and Minar goes against Monaco in Sunday's reverse singles.
Argentina is making its eighth consecutive Davis Cup quarterfinal appearance and last played the Czech Republic in the tournament in 2005, when the Argentines won 5-0.
Argentina and the Czech Republic are playing for a Davis Cup semifinal berth in September against either Croatia or the United States.