The rockers from the French Basque town of Bayonne have been nominated in two categories including the coveted Best Rock Album for Magma.
"We started playing pretty intense thrash and death metal and I've been mostly growling for the last 20 years, so I wasn't expecting any kind of award," Gojira's 40-year-old frontman and rhythm guitarist Joe Duplantier told the AFP news agency with a small laugh.
"I never even thought of the concept of being nominated for the Grammys," he said.
Gojira -- whose name is the Japanese for Godzilla -- edged a small step into the mainstream with Magma.
The group was previously known for raw, complex songs that built to a dark climax but Magma is more accessible with chorus structures and Duplantier at times swapping growls for clean vocals.
The Grammys are not the only recognition that Gojira has received recently. Metal legends Metallica, whom Duplantier counts as a key influence, earlier tapped Gojira as an opening act.
Metallica lead guitarist Kirk Hammett in a recent interview with AFP said Magma was "incredible" and "the best thing I've heard in a long time".