Manchester United central defender Maguire has won 66 international caps and been a mainstay of England's back line at recent tournaments, but has barely featured since missing out on the last European Championship due to injury.
Maguire announced the news in an emotional Instagram post on Thursday.
"I was confident I could have played a major part this summer for my country after the season I've had. I've been left shocked and gutted by the decision," the 33-year-old wrote.
"I've loved nothing more than putting that shirt on and representing my country over the years. I wish the players all the best this summer."
Maguire was considered a shoo-in by many after a resurgent season at United as a key part of his team climbing to third in the Premier League and clinching a return to the Champions League. His Manchester United teammate Luke Shaw has also been left out of the England squad, according to reports.
Foden and Palmer, like Maguire, were called up by Tuchel for the March friendlies against Uruguay and Japan, in which an experimental England side failed to impress.
After the 1-0 loss to Japan, Tuchel said Foden could not be sure of going to the World Cup having struggled for game time at Manchester City.
Foden has started one Premier League game since while Palmer has failed to replicate the prolific scoring form he showed last season at Chelsea.
Ivan Toney has been named in the squad, the reports said, after the 30-year-old former Brentford striker netted 32 goals in 32 Saudi Pro League games for Al Ahli this season.
Tuchel reportedly made calls on Thursday to players who did not make the cut for the tournament in the US, Canada and Mexico, where England face Croatia, Ghana and Panama in Group L.