The Navy said in a statement posted on Twitter that officials became aware of the video on Sunday.
The videos were apparently posted on Instagram last year and resurfaced over the weekend.
"The inherent message of this video is completely inconsistent with the values and ethos of Naval Special Warfare and the U.S. Navy," the statement said.
The Navy said the "initial indications" are that no active duty personnel or equipment were used in the demonstration at the "independent organization's event."
The Navy Seals Museum is located in Fort Pierce, Florida, which is north of West Palm Beach on the state's Atlantic Coast.