The 20-year-old Klinsmann, who has made six appearances for Hertha's Under-23 side in the fourth-tier regional league, will play alongside Socceroos star Mathew Leckie.
Klinsmann is getting his chance with the senior team as regular goalkeeper Rune Jarstein skips Hertha's international games, while his back-up Thomas Kraft is out with a cold.
Hertha is already out of the Europa League, so only pride is at stake against Ostersund.
"Jonathan has developed well. He looks good and is much better in training, from his stability and control," Hertha coach Pal Dardai said.
"There's pressure. He has to show he can live with the name."
Jurgen Klinsmann, a prolific striker who won the World Cup with West Germany in 1990, coached Germany when it hosted the tournament in 2006.
He took over the U.S. national team in 2011 and coached the side for five years.
Jurgen's son stands at 1.94-metre tall, a goalkeeper with the United States Under-20 team, and was handed his first professional contract after impressing Hertha during a trial in the off-season.
He previously played for the University of California.