The banner, which said "North Carolina Cheeseheads," was made Monday and shipped to Mike Dobs in Fayetteville, North Carolina.
Team officials had no further comment on the situation. Newton also declined to comment on it, saying he was focused on Sunday's game against the Tennessee Titans.
Newton tore down the banner during warm-ups, saying it didn't "fit" in Carolina's home stadium and he was protecting "this house."
"It's just a respect thing," Newton said.
Dobs, a Wisconsin native and retired Army command sergeant major working at Fort Bragg, contacted stadium security and reported the banner he paid $500 for as stolen. He told the Fayetteville Observer he was "just shocked, shocked."
Carolina coach Ron Rivera said on Monday that the matter was being taken care of. He also wouldn't address it further, saying his focus was on getting the Panthers to 9-0 at Tennessee.