"Part of me feels like I need to go around to every single Indian person in this country and personally apologize," said the "Simpsons" cast member.
The character Apu Nahasapeemapetilon has been criticized for reinforcing Indian stereotypes.
Cronica TV captioned the picture "Apu Arrives" -- and faced immediate backlash over the imagery.
The rumor comes from TV and film producer Adi Shankar -- although "Simpsons" executive producer Al Jean says Shankar "does not speak for our show."
Matt Groening's comments come as Hank Azaria, who voices Apu, said he'd be happy to "step aside" from the role.
"The idea that anyone young or old, past or present, being bullied based on Apu really makes me sad."
The star of "The Problem With Apu" documentary said the show's response was a slap "at what many of us consider progress."
“I think the documentary made some really interesting points and gave us a lot to think about and we really are thinking about it,” Azaria said.
Comedian Hari Kondabolu speaks with other South Asian stars on "The Simpsons" character and representation on-screen.
Comedian Hari Kondabolu once said Apu's voice sounds like “a white guy making fun of my father.”