Jewish groups had complained that the caricature resembled Nazi propaganda.
Cartoonist Burkhard Mohr said he had intended to illustrate Facebook swallowing up rival WhatsApp.
The cartoon was published last Friday in early editions of daily Sueddeutsche Zeitung. Later editions showed an empty hole where Zuckerberg’s face had been.
“I’m very sorry about this misunderstanding and any readers’ feelings I may have hurt,” Mohr said in an email to the Associated Press news agency.
“Anti-Semitism and racism are ideologies that are totally alien to me.”
Sueddeutsche Zeitung has been criticised in the past for appearing to defame Jews.
Last July it apologised after printing a picture caption that likened the state of Israel to a ravenous monster.-BBC