World number two Alcaraz pulled out of last month's Barcelona Open after suffering the injury in the first round of the clay event.
The problem then forced the 23-year-old out of the Italian Open and French Open, where he is the two-time defending champion.
"My recovery is going well and I'm feeling much better, but unfortunately I'm still not ready to compete, which is why I have to withdraw from the grass-court swing at Queen's and Wimbledon," Alcaraz posted on Instagram.
"They are two truly special tournaments for me and I will miss them a lot.
"We'll keep working to come back as soon as possible."
Alcaraz attempted to win a third straight Wimbledon title last year, but fell in the final at the hands of rival Jannik Sinner.
The Spaniard started this year by winning the first major of the tour at the Australian Open to become the youngest man to complete the career Grand Slam.
Alcaraz, who has seven major titles, lost the world number one rank to Sinner after being beaten by the Italian in April's Monte-Carlo Masters final.
Sinner will now be the heavy favourite to retain his Wimbledon crown after taking down Alcaraz in last year's final.
The 24-year-old is also well placed to win the French Open for the first time and complete the career Grand Slam himself.
He has won three clay tournaments heading into Roland Garros, where he lost last year's final to Alcaraz in a five-set thriller.