Kalou posted a live video of himself on Monday singing a ‘corona song’ while interrupting the Covid-19 test of a teammate, and was also seen shaking hands with his colleagues.
The Bundesliga has been suspended since March but it set to bounce back on May 16 or May 23 after a May 9 resumption date was delayed by the government.
In accordance with plans to restart the season, 1,724 tests conducted on players and staff from Germany’s top two divisions showed 10 positive cases of Covid-19.
A Hertha statement read: "Salomon Kalou was tempted by his negative test results to greet the other players in the dressing room, sometimes with a handshake, contrary to the clear announcements made by health authorities.
"With his 'Corona Song', Kalou gave the impression that he is not aware of the extent of the ongoing pandemic.
"With this video taken inside the team's dressing room, Kalou broke clear internal rules and displayed a behaviour, which is neither appropriate for this current situation, nor reflective of the code of conduct of Hertha BSC.
"The club has therefore made the decision to suspend the player in question from training and matches with immediate effect."
The 34-year-old, who won the UEFA Champions League with Chelsea in 2012, has apologised for his actions in a message posted on Hertha Berlin’s official website.
"I'm sorry if I gave the impression that I'm not taking coronavirus seriously. I want to apologise for this,” the statement read.
"The reality is the exact opposite, because I'm really worried about the people of Africa, because health systems aren't as good there as they are in Germany.
"I didn't really think it through, and was excited that my tests came back negative.
"I would also like to apologise to all those who appeared in the video who didn't know that I was broadcasting live and whom I didn't want to bring into this situation."