The flight reportedly took place on Dec. 6.
The photo shows someone wearing a Burger King crown with the statement "Ye is right," referring to the rapper formerly known as Kanye West. The Simon Wiesenthal Center said the phrase, "white power" was also written on the crown.
The Simon Wiesenthal Center said Southwest should reassure flyers it won't tolerate bigotry by passengers.
Eyewitness News reached out to Southwest Airlines but have not heard back.
MORE | Demonstrators on 405 overpass express support for Kanye's antisemitic remarks
Demonstrators on 405 Freeway overpass express support for Kanye West's antisemitic remarks