"It's a stunning thing, that a white supremacist would be a permanent member of the National Security Council," Pelosi said at her weekly news conference.
The move is "making America less safe," the California Democrat added.
The Democratic National Committee doubled down on that criticism Friday, labeling Bannon Trump's "white supremacist chief strategist" in an email and asking recipients to demand his resignation.
Pelosi has been critical of early moves by the Trump administration, but she also Thursday seemed to raise question about the President's fitness for the job.
She brought up a proposal that House Oversight Chairman Jason Chaffetz, R-Utah, was reportedly considering that would require an independent medical assessment of the condition of the President, including mental health.
"If you're going to have your hands on the nuclear codes, you probably -- we should probably know what mental state you're in," Pelosi said.
"I can't wait until he introduces that legislation, to be able to join him as cosponsor of that," telling reporters, "I think it's a very good idea."
When asked about her early overtures to Trump -- attending the inauguration and expressing willingness to work with the new President -- Pelosi cautioned reporters: "Please don't mistake courtesy for approval or anything else positive."
Pelosi repeated her vow that she and her party would fight the Republican effort to dismantle the health care law. She criticized the administration's decision to stop paying for advertisements ahead of the Obamacare enrollment deadline and predicted about the Republican effort to do away with the law.
"This will lead to suffering, death, disability," Pelosi said.