Spokesman Joern Wolf says Rajkovic will "not take part in the upcoming trip to South Korea" from Monday until 25 July.
Son also faces punishment over the incident with Rajkovic, which started with a war of words before becoming physical.
Uninvolved midfielder Tolgay Arslan was injured when Son tried to evade Rajkovic and collided with Arslan.
Also on Friday, a local investor into the club, billionaire Klaus-Michael Kuehne, said he was ready to help the cash-strapped club again if it made an effort to lure Dutch playmaker Rafael van der Vaart back to the club he played for between 2005 and 2008.
"I want to see a good and strong team. Hamburg must land a big transfer because that will attract other good players as well," Kuehne said.
Hamburg sports director Frank Arnesen named a transfer of Van der Vaart too expensive and Van der Vaart told the Bild daily he was staying at English club Tottenham Hotspur.