The Spaniard confirmed at the Madrid Open press conference on Thursday that he was withdrawing from the tournament due to both the abductor injury that hampered him in the Barcelona Open final, and a separate issue - also believed to be an abductor - in his left leg.
"I couldn't practice the entire week and found out I had hamstring and groin injuries," said the four-time grand slam winner.
"I needed to listen to my body and make the right decision. On Monday, I'll have more medical tests and after that we will have a better idea on how long I'll be out.
"This tournament is very exciting, but things haven't worked out the way I wanted to be able to compete. It hurts me not to be able to play here in Madrid in front of my people, my friends and my family.
"In a week or two I shall return to training, but I will take it step by step. I needed to listen to my body and make the right decision.
"I don't want to get too far ahead but I hope I shall be ready for the French Open."
Alcaraz is a two-time Madrid Open champion and reached the quarter-final of the event back in 2024, ultimately losing to eventual champion Andrey Rublev in three sets.
His withdrawal is set to have a significant impact on the ATP Rankings, with both Alexander Zverev and the absent Jannik Sinner in line to benefit from the Spaniard's withdrawal.
Having reached the last eight in 2024, Alcaraz had 200 ranking points to defend heading into 2025.
Now unable to defend those points, the 21-year-old will fall from 8,050 points to 7,850 points once the tournament is over.
Alcaraz is guaranteed to stay as the world No. 3, with world No. 4 Taylor Fritz only able to hit a maximum of 5,715 points with a hypothetical run to the title.
However, he will now be unable to close the gap to world No. 1 Sinner - and could lose further ground in his battle with world No. 2 Alexander Zverev.
Having briefly fallen to world No. 3 post-Monte Carlo, Zverev returned to world No. 2 this week following his triumph in Munich - with Alcaraz unable to lift the title in Barcelona.
Now, the 28-year-old has been handed the chance to build his cushion over Alcaraz with a strong run in Madrid.
Heading into the tournament, Alcaraz was only 35 points off Zverev's haul of 8,085 ranking points.
However, the German already had a slight advantage heading into action inside the Caja Magica, with only 100 points to defend after a fourth-round exit in 2024.
Currently earning just 10 points, Zverev is projected to fall to 7,995 points in the ATP Live Rankings.
However, the German is yet to compete in Madrid and could be primed for a significant surge, potentially leading Alcaraz by over 1,000 points once the tournament is over.
Should top seed Zverev lift the title in Madrid, he would surge to 8,985 ranking points, a hypothetical lead of 1,135 points over the Spaniard.
Though the German would then have to defend 1,000 points as the reigning Italian Open champion, it would give him a significant cushion over Alcaraz in the race to be seeded second at Roland Garros.
Zverev was the Madrid Open champion in 2018 and 2021, meaning a deep run would not come as a surprise in the slightest.
Sinner's three-month suspension from the ATP Tour has largely been defined by both Alcaraz and Zverev failing to put pressure on his world No. 1 ranking.
And, with Alcaraz out of Madrid, he has been handed another significant advantage.
A quarter-finalist in Madrid twelve months ago, Sinner will drop 200 points to 9,730 when the rankings update post-tournament.
However, with Alcaraz also dropping the same number of points, that means the current gap of 1,880 points between the two will remain.
That is of huge significance for Sinner, who has no points to defend at the Italian Open following his 2024 withdrawal and fewer points to defend at Roland Garros than reigning champion Alcaraz.
With the Spaniard also having no Italian Open points to defend, but a staggering 2,000 points at Roland Garros, he cannot overtake Sinner as the world No. 1 this clay swing.
And, as Zverev has Rome champion and Roland Garros finalist points to defend, Sinner is mathematically guaranteed to still be world No. 1 once the second Grand Slam of 2025 is complete in early June.
Having risen to the top of the ATP Rankings after the French Open in 2024, that ensures that the Italian will have reigned as world No. 1 for a whole calendar year.
He will become just the fifth man in ATP Rankings history to reign for 52+ weeks in his first spell as No. 1, and just the 10th to spend 52+ consecutive weeks overall.