Schoenmaker is the second South African female swimmer to win an Olympic medal since Penny Heyns' bronze at the 2000 Sydney Olympics.
After setting an Olympic record in the 100m heats (1:04.82), Schoenmaker just fell short of gold in the final.
Swimming in lane four, Schoenmaker was first after the 50m turn but 17-year-old Lydia Jacoby of America surpassed her, and she eventually finished second, putting Team SA on the board in Tokyo.
Schoenmaker touched the wall in 1:05.22 - 0.27 seconds behind Jacoby (1:04.95) as world record-holder Lily King (1:05.54) finished third.
Schoenmaker will now turn her attention to the 200m breaststroke heats, scheduled for Wednesday (12:49 SA time).
Later in the day Bianca Buitendag bagged another medal for Team South Africa in the women's surfing. The final of the surfing was brought forward by a day due to concerns over a storm approaching, and Buitendag had earlier continued her good form on Tuesday when she moved past Portugal's Yolanda Hopkins and America's Caroline Marks in the quarter-final and semi-final, respectively.
In the gold medal match, Buitendag lost out to America's Carissa Moore, going down 14.93 to 8.46.
