Vogt went 0-for-4 on Sunday and caught the entire game in a 6-3 victory over the Angels, despite arriving at the ballpark less than an hour before first pitch.
The left-handed hitter was batting .364 with three home runs and 19 RBIs at Sacramento, including .433 with 15 RBIs over his last 14 games.
"We're a little beat up on the bench right now, with Reddick being out, Moss being out. I wouldn't consider [infielder Nick] Punto [left calf] yet 100 percent," Melvin said. "Stephen was doing really well. We always knew that he'd be here at some point."
Asked whether Vogt's promotion is a short-term or long-term move, Melvin declined to specify.
"He's a guy that's been here before, been instrumental for us, and he is here right now," he said.
As for Rodriguez, Melvin said the right-hander was a victim of circumstance.
"He's done a great job for us, and really he didn't do anything to deserve to be sent down," Melvin said. "You look at his numbers, he's got a [1.13] ERA, he's done everything we've asked him to do, pitched in some important games for us.
"Still not able to go back-to-back games coming off Tommy John surgery, so we needed the spot. Unfortunately it was him."
Vogt appeared in 47 games for Oakland in 2013, hitting .252 with four homers and 16 RBIs.
Aaron Leibowitz is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.