Tampa Bay also designated reliever Winston Abreu for assignment and activated reliever Chad Bradford off the DL.
Kazmir, who has missed 32 games with a right quadriceps strain, will start against the Marlins on Saturday.
Sonnanstine went 13-8 with a 4.38 ERA last season, but he was erratic this season. His 6.61 ERA, 11.35 hits per nine innings pitched and 60 runs allowed were all the highest in the Major Leagues.
Sonnanstine allowed four runs in the first inning to Philadelphia on Thursday but settled down to get the win after 5 1/3 innings. His six wins are tied for the team lead.
Rays manager Joe Maddon said the decision to send him to the Minor Leagues was primarily based on wanting to give him more opportunities to pitch.
"You look at his numbers overall, his hits per innings pitched, et cetera, he's better than that," Maddon said. "We just want him to go down and get his innings and keep pitching and kind of step back from the situation right now and get himself back to where he had been at the end of the last season. I believe he will be."
Abreu, a 32-year-old journeyman with his third professional franchise, made two appearances for the Rays and allowed one run on three hits in 3 2/3 innings.
"This young man has pitched very well," Maddon said. "He's done a great job for us in Durham. This is a wonderful young man and we see him as being part of our future."
Maddon reiterated that he wants Sonnanstine to rediscover his form and be able to rejoin the club later in the season.
"I have a lot of respect for this guy and I have a great relationship with him," Maddon said. "I told him that him coming back and helping us at some point this season is going to be a big factor in us getting back to the World Series."
Zach Schonbrun is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.