Minter had been out since July 12 while recovering from left shoulder inflammation. He will return to his late-innings role in the Braves' bullpen for Monday night's opener of an interleague series against the Los Angeles Angels.
Minter is 3-5 with a 4.91 ERA and 10 saves.
Smith-Shawver, a 20-year-old rookie, allowed three runs in five innings and did not receive a decision in Sunday's 8-6 win over the Milwaukee Brewers on Sunday. He is 1-0 with a 4.56 ERA in five games, including four starts.
Smith-Shawver's spot in the rotation could be filled by the expected return of left-hander Max Fried from the injured list. Fried has been out since May 6 with a strained left forearm.
Also, infielder Charlie Culberson was designated for assignment to clear a roster spot for infielder Nicky Lopez, who was acquired from the Kansas City Royals in a trade for left-hander Taylor Hearn on Sunday.