Bobic slammed the Gunners ace over his retirement from the German national team, citing racism as part of the reason for his decision.
"I think that's a bit cowardly," he told Bild. "Ozil's criticism of social media, especially in the direction of the German Football Association (DFB), is unbearable.
"This blanket charge of racism simply does not correspond to reality. He could have given an interview somewhere, live on TV.
"For us footballers, the rule is 'be a man and stand up.'"
Bobic also believes Ozil's photo with Turkish president Recep Tayyip Erdogan was a major mistake, which he believes was "either totally naive" or saw Ozil purposely look to be "provocative".
"I would allow that to a player who is 18 or 19 years old, but a player who has been in the business for so long, 29 years old and world champion, needs to know what this looks like," Bobic said.
"If he does not know that, then he is either totally naive - I cannot imagine that - or it is calculating and he wanted to be provocative, or else he is alienated, of course.
"I understand the two hearts that beat in his chest, but nevertheless, you must know that you have a great responsibility."