Ferrer, twice a quarter-finalist at the grasscourt slam, was leading 3-0 when Belgium's Darcis cried off with a back injury.
Darcis, who once beat Rafa Nadal at Wimbledon, is the eighth player to retire in the men's singles at this year's championships.
Two players - Martin Klizan and Alexandr Dolgopolov - failed to complete their matches on Centre Court against Novak Djokovic and Roger Federer respectively on Tuesday.
Unseeded Ferrer will play either Czech Tomas Berdych or American Ryan Harrison in the third round.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
(Reporting by Martyn Herman; Editing by Louise Ireland)
