Alvarez will replace injured Washington pitcher Jordan Zimmermann for Tuesday night's All-Star game at Target Field in Minnesota.
Zimmermann left Friday night's start against Philadelphia after 3 1-3 innings because of a right biceps injury. The roster change was announced Saturday.
Rodney will take the spot of Tampa Bay lefty David Price. Because of an illness, Price was pushed back in the Rays' rotation to start Sunday, making him ineligible for the game.
Alvarez, a first-time All-Star, is 6-4 with a 2.63 ERA and three shutouts in 19 starts. He pitched a no-hitter against Detroit on the final day of the 2013 regular season.
''I'm happy. I'm excited to receive the news today,'' Alvarez said through a translator at Citi Field, where the Marlins played the New York Mets. ''It's very emotional for me. ... At first when they announced the All-Star roster, I was a little bit disappointed.''
The 24-year-old Alvarez has been Miami's top starter since 2013 NL Rookie of the Year Jose Fernandez went down with a season-ending elbow injury in May.
''We talked about a guy stepping in, and Henderson's definitely done that,'' manager Mike Redmond said. ''It's great to see these guys step up and get recognized for their work, and it's been fun to watch Henderson develop. You think back to last year when he threw the no-hitter at the end of the season, I think that's just kind of been a catapult for him and has led to the success he's had this year.''
Alvarez went nine games in a row without allowing more than two runs before his 7-1 loss to the Mets on Friday night.
''It's great to see him get in. Definitely deserved it. He did a great job,'' Redmond said.
The 37-year-old Rodney is a two-time All-Star and leads the AL with 27 saves. He was previously Price's teammate with the Rays.
Rodney likes to punctuate his saves by pretending to fire up his bow.
''I'm going to have fun. I'll throw my arrow,'' he said. ''No matter what inning I pitch, I'll throw it.''
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