Motsau, 23, was edged out in a blanket finish, as he crossed the line in 3:39.51, taking third place to lift the country's tally to six medals after four days of competition in Kazan, Russia.
Valentin Smirnov, representing the host nation, secured the gold medal in 3:39.39.
"I didn't expect a medal because it's my first World Student Games, so I'm very grateful," Motsau said.
Shortly after his race, Motsau boarded a plane to Brussels, where he will compete on Saturday in an attempt to qualify for next month's IAAF World Championships in Moscow.
Meanwhile, Anneri Ebersohn finished an impressive fifth in the women's 400m hurdles final in 57.58 seconds. Anna Titimets of the Ukraine won gold in 54.64.
Earlier, PC Beneke comfortably won his semi-final in 49.91 seconds to qualify for Wednesday's final in the men's 400m hurdles.
Anaso Jobodwana, who won gold in the men's 100m sprint earlier in the week, and Gideon Trotter both qualified for the men's 200m semi-finals.
Jobodwana won his second-round heat in 20.76 seconds, while Trotter was third in his heat in 21.07.
Arista Nienaber (24.11) and Justine Palframan (24.43) also progressed to the semifinals of the women's 200m event, taking second place in their respective heats.
The SA women's football team put up another brave showing to reach the quarterfinals with a 3-2 win over Chinese Taipei in their last Group A match.
Noko Matlou, Leandra Smeda and Sanah Mollo all found the back of the net as South Africa progressed on points difference.
They will face Japan on Thursday for a place in the semi-finals.
In judo, Seamus Mingay beat Ka Leong of Macau to reach the last 16 in the men's Under-66kg event.
He lost, however, to Rishad Sobirov of Uzbekistan in the next round.