Nadal was forced to skip the Masters 1000 event in Indian Wells last month as well as the Miami Open that ended last week, as he continues his recovery from a hip issue that ended his Australian Open title defence in the second round in January.
"Unfortunately I am still not ready to compete and will miss one of those special tournaments I always love to play," Nadal said in a statement.
"Monte Carlo is and has been a key event in my career, but unfortunately I will have to miss it again since I am still not ready to compete without the risk of getting injured. I will continue the process of getting ready to come back."
His absence from competitions means that Nadal days ago dropped four places to 13th in the rankings, ending his record 912-week stay inside the top 10.
The Mallorcan, who has won Monte Carlo 11 times in his career still hopes to be fit for the French Open in May, a clay court tournament he has dominated for years, having won there 14 times.
Alcaraz, who had an injury-plagued start to the season, will also miss the tournament. The 19-year-old was last in action last week at the Miami Open, where he was beaten in the semi-final by Italian Jannik Sinner.
"After two months of competing, I am happy to be back home but sad that I finished my semi-final match in Miami with discomfort," the U.S. Open champion said in a post on social media.
"After visiting my doctor today ... and being evaluated, I won't be able to go to Monte Carlo to start the clay court tour.
"I have post-traumatic arthritis in my left hand and muscle discomfort in my spine that needs rest to cope with all that is to come."
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