The 23-year-old seven-time Grand Slam champion has not played since withdrawing from the Barcelona Open last month.
"My recovery is going well and I feel much better but unfortunately I'm still not ready to be able to play, and that's why I have to withdraw from the grass-court swing at Queen's and Wimbledon," the 2023 and 2024 Wimbledon champion wrote on X.
Alcaraz's rivalry with world No 1 Italian Jannik Sinner has captivated men's tennis and his absence from the next two Grand Slam tournaments is a huge blow to fans and broadcasters alike.
The pair contested an epic French Open final last year with Alcaraz coming back to win the title before Sinner turned the tables to take the Wimbledon crown.
Sinner has the chance to complete his Grand Slam haul at Roland Garros after ticking off a full set of Masters 1000 titles earlier this month, and the withdrawal Alcaraz has changed the feel of the tournament.
Alcaraz became the youngest man to complete the career Grand Slam this year when he won the Australian Open but now faces the prospect of a drop down the ATP rankings.
That will be less of a concern to Alcaraz though than ensuring his wrist is completely healed before returning.
He appeared at this year's Laureus World Sports Awards with a cast on his injured wrist.
Speaking at that event, he said: "I'd rather come back a little later and with a full recovery. I need to take care of myself because I want to have a long career."
His absence from Wimbledon will make Sinner the overwhelming favourite to defend his title.
The French Open main draw gets under way at Roland Garros on Sunday while Wimbledon starts on June 29.
