Mike Yastrzemski, 28, was acquired by the Giants from the Baltimore Orioles in March. He hit .316 with 12 home runs and 25 RBIs in 40 games for the River Cats this season.
Outfielder Mac Williamson was designated for assignment in a corresponding move. Williamson hit only .118 with one home run and seven RBIs in 15 games.
Mike Yastrzemski went 0-for-3 in the Giants' 10-4 loss to Arizona on Saturday. He was hit by a pitch in the seventh inning and scored on Evan Longoria's walk later in the frame.
Mike Yastrzemski is the latest player with Hall of Fame bloodlines to reach the major leagues. Carl Yastrzemski played 23 seasons for the Boston Red Sox from 1961 to 1983.
"Yaz" was an 18-time All-Star. He won the AL Triple Crown in 1967.
Toronto also promoted Vladimir Guerrero Jr. to the big leagues on April 26. Vlad Sr. was inducted into the Hall of Fame last summer.
San Francisco fell to 21-30 with Saturday's loss.