The world number two withdrew from last month's Barcelona Open after sustaining the injury to his right wrist in the first round.
The Spaniard subsequently pulled out of the French Open, where he is the two-time defending champion, to recover.
"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 wrote on Instagram on Tuesday.
"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."
