The Real Madrid forward, who hasn't been picked for France in five years, said Giroud was a like go-kart while he was playing at Formula One level.
"You don't compare Formula 1 with karting, and I am being nice," Benzema said.
Griezmann, who played alongside Giroud when France won the World Cup in 2018, responded to Benzema's comments on Twitch.
"I can't answer all that, that could get me into trouble," Griezmann said.
"I love Olivier Giroud, he's a good player and he helped us win the World Cup. And that's important in life."
However, Benzema doubled down on his comments following Griezmann's involvement.
"About Giroud, I simply told the truth," Benzema said. "But we didn't remember what I said about him, especially about what he brings to the French national team.
"We just remembered the moment when I said I was F1 and he was karting.
"That's what I think, that's the truth, and that's how it is."