The stencil had been on display near the centre in central Paris, where it was protected by a plastic shield. But now it has disappeared.
The image of a masked rat holding a knife was painted on the back of a traffic sign in Paris' 4th arrondissement, media reports said.
Banksy, who keeps his identity a closely guarded secret, rarely confirms whether he is behind works of street art, but he had shared an image of the Paris sketch on his Instagram feed back in 2018.
In his post on Instagram, Banksy had said: "Fifty years since the uprising in Paris 1968. The birthplace of modern stencil art."
Following the "theft", the Pompidou Centre said in a statement on Twitter: "Although this piece was not part of our collections, we were proud that the artist had chosen the side of our building to create it, as an hommage to the events of May '68."
The Pompidou Centre said it was taking legal action over the piece's disappearance.
The police confirmed that the artwork had gone missing some time overnight on Sunday, and an investigation was underway.
The French capital hosts several works of art by Banksy, born in the UK in 1974 and whose identity is not publicly known.
( With inputs from IANS )