The comments from the Foo Fighters founder came in an eight-minute recording as part of a series called "Dave's True Stories", which has been keeping fans entertained during the coronavirus lockdown.
In the first audio version of the series, titled "In Defence of Our Teachers", Mr Grohl recalls his memories of growing up while his mother taught in schools.
"As a single mother of two, she tirelessly devoted her life to the service of others, both at home and at work,” Mr Grohl said, before recalling the multiple jobs she worked to help support the family.
"Unsurprisingly, her devoted parenting mirrored her technique as a teacher. Never one to just point at a blackboard and recite lessons for kids to mindlessly memorise, she was an engaging educator, invested in the wellbeing of each and every student who sat in her class."
Mr Grohl took aim at the Trump administration's plans to reopen schools in September.
He said: "America’s teachers are caught in a trap, set by indecisive and conflicting sectors of failed leadership that have never been in their position and can’t possibly relate to the unique challenges they face."
He added: "Until you have spent countless days in a classroom devoting your time and energy to becoming that lifelong mentor to generations of otherwise disengaged students, you must listen to those who have.
"Teachers want to teach, not die, and we should support and protect them like the national treasures that they are. For without them, where would we be?"
The musician also raised concerns about the lack of resources available to schools.
"Most schools already struggle from a lack of resources," he said. "How can they possibly afford the mountain of safety measures that will need to be in place?”
He concluded: "Remote learning is an inconvenient and hopefully temporary solution, but as much as Donald Trump’s conductor-less orchestra would love to see the country reopen schools in the name of rosy optics, ask a science teacher what they think about White House press secretary Kayleigh McEnany’s comment that ‘science should not stand in the way.’
"It would be foolish to do so at the expense of our students, teachers and school."
Earlier this month, Mr Trump said pressure will be put on state governors to reopen schools in September, as he continued to claim that some have remained closed for "political reasons".
"They think it's going to be good for them politically, so they keep the schools closed," the president said at a White House discussion on school plans.
"No way. We're very much going to put pressure on governors and everybody else to open the schools."
But the president of the nation's largest education union said Mr Trump is "more interested in scoring points for the November election than in keeping students safe".