The 20-year-old Briton, currently world number 85, was poised to face Bulgaria's Viktoriya Tomova in the Spanish capital, ahead of a potential clash with world number one Iga Swiatek in the second round.
The Briton was replaced by Austrian lucky loser Julia Grabher.
Raducanu has been beset by health problems this year, suffering from a wrist injury during her first-round defeat by Bianca Andreescu in the Miami Open in March.
"I'm able to play in the short-term, but the current solutions aren't very viable long-term," said Raducanu after defeat in Miami.
Raducanu, who has also suffered from tonsillitis, has only played 10 matches this season and won five.
She withdrew from events in Auckland and Austin earlier this year and will now be targeting Rome and the French Open, which starts May 28th.
Raducanu had told reporters in Madrid her wrist was "OK" amid a tense news conference Tuesday.
Since becoming the first qualifier in history to win a Grand Slam, Raducanu has burned through a string of coaches, currently working with Sebastian Sachs.
