Weaver struck out nine and walked one. The Twins never came close to getting a hit against the All-Star right-hander.
Phil Humber of the Chicago White Sox threw a perfect game against Seattle on April 21.
Weaver (4-0), a California native who played at Long Beach State, quickly retired Jamey Carroll on a routine fly and struck out Denard Span looking to begin the ninth.
Weaver then got Alexi Casilla to lift a long fly that right fielder Torii Hunter easily caught at the warning track. The Angels' ace watched his Gold Glove outfielder make the play, then put his hands on his head as the Angels rushed out to mob him.
His gem complete, Weaver hugged his wife, his dad and his mom, who was crying on the field.
"I'm at a loss for words right now. It hasn't kicked in yet," Weaver said. "Thank you for all your support. Couldn't have done it without the defense. The guys were picking me up left and right.
This was the second Angels no-hitter in less than a year - Ervin Santana pitched one July 27 at Cleveland.