The second-seeded Berdych, fresh off his title in Montpellier, France two weeks ago, was leading former Australian Open runner-up Marcos Baghdatis 3-0 in the first set on Thursday when the Cypriot retired due to a calf injury.
The third-seeded del Potro popped nine aces in handling Slovakian qualifier Karol Beck 6-4, 7-5.
Viktor Troicki, the No. 7 seed, handled Jesse Huta Galung 7-6 (7-2), 6-3. The Serbian will face del Potro in the quarters.
Fifth-seeded Frenchman Richard Gasquet secured a berth in the quarters with a 6-3, 6-2 victory over Russian Alex Bogomolov Jr. on the indoor hardcourts at Ahoy Stadium. Gasquet's opponent on Friday will be fellow former top-10 star Nikolay Davydenko of Russia.
The top-seeded former world No. 1 Federer received a walkover into the round of eight here on Wednesday night when Russian Mikhail Youzhny pulled out of their scheduled Thursday second-round match, citing a left foot injury. Youzhny was the Rotterdam champion in 2007 and runner-up in 2010.
The 16-time major champion Federer was the Rotterdam titlist the last time he played here back in 2005.
The 2012 Rotterdam winner will collect $385,000.