Djokovic (35), who was unable to play in the US hard court swing earlier this year because he has not been vaccinated against COVID-19, hasn't made a strong start to the clay court season, being knocked out early at the Monte Carlo Masters and Banja Luka Open.
The world number one has been struggling with an elbow injury and has admitted he's not playing well at the moment.
"I didn't feel well on the court, my legs were slow and my footwork was torpid, many missed shots, totally without direction," said the Serb after his quarter-final defeat by Dusan Lajovic (32) at the Banja Luka event.
Djokovic said, however, that he was still hopeful of finding his groove on clay before next month's French Open, but won't be doing so at the Madrid Open.
"Wishing you a speedy recovery, we hope to see you back on court as soon as possible, Nole," Madrid organisers said in a statement without giving any details on Djokovic's condition.
Nadal announced earlier this week that he would miss the Madrid tournament after a setback in his recovery from a hip injury sustained at the Australian Open in January.
The two players share the record for most Grand Slam titles, with 22 each. The French Open, the second Grand Slam of the season, begins on May 28.