Branyan will relieve third baseman Bill Hall of his duties during Sunday's game against Washington. Hall has struggled against right-handed pitchers, hitting just .159 against them as opposed to .415 against lefties.
"Branyan is swinging the bat very well in Triple-A," Yost said. "We're just looking for a little offense."
The left-handed hitter is fifth in the Pacific Coast League with a .359 batting average. He's hit 12 home runs and his on base plus slugging is 1.145.
Gwynn had started just six games this season, and Yost felt that without regular work, there was the risk that the young player's skills would start to diminish.
"We have a lot of plans for Tony in the future, and we don't want him sitting here losing his skills," the manager said. "It's tough, but he's gotta play. It's not fair to him, and it's not fair for us to let him sit here."
Yost emphasized that if a need arose, the team would not hesitate to call Gwynn up.
New addition Branyan has bounced around between Major League teams, playing for three last season alone. He was a Brewer during the 2004 and 2005 seasons.
He'll start at third base in Sunday's game against Washington, which is using right-handed pitcher Tim Redding.
In addition to struggling at the plate, Hall also had a rough night in the field Saturday, and committed two errors in the ninth inning to allow Washington to get the tying run to the plate.
Branyan and Hall could enter a platoon situation, though Yost has yet to make a firm decision on that at this time.
Michael Phillips is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.