She ended by re-enacting receiving a fatal gunshot to the head at the spot in Dallas where President John F Kennedy was assassinated in 1963.
Sergeant Warren Mitchell said Badu was charged after a witness offered a sworn statement to police. Badu's spokeswoman made no immediate comment.
The singer, who was born in Dallas, performed a walking striptease in front of tourists and pedestrians during the shoot in Dealey Plaza on 13 March for her video for the song Window Seat.
Sgt Mitchell added that the police department has had "people calling from all across the country to express their concern".
"Having a fact witness that was there, is what let us file the charges," he said. "After much discussion, we feel that these charges best fit her conduct. She disrobed in a public place without regard to individuals and small children who were close by."
He said Badu can either fight the charge or pay the fine. Disorderly conduct is punishable by a fine of up to $500 (328).
Badu's highly acclaimed debut album was released in early 1997 and debuted at number two on the Billboard charts. Lead single On & On reached number 12 on the singles charts in both the US and UK. Badu received notice for her introspective lyrics and jazzy, bass-heavy sound, and was hailed as one of the leading lights of the burgeoning neo soul genre. Her sophisticated style of singing drew many comparisons to Billie Holiday.
Baduizm eventually went triple platinum and, along with On & On, won a Grammy Award.
Badu became involved with rapper Andr 3000 of OutKast, with whom she had a child, Seven, who was born in 1997.
The singer recorded her first live album, Live, while pregnant with Seven, and the release of the recording coincided with the birth of her child.