As investigators try to figure out who is behind the recent massive hacking attack on Sony Pictures Entertainment, there’s a new mystery: who sent the threat to attack theaters that show Sony’s comedy about an assassination plot against North Korean leader Kim Jong Un and how seriously should the warning be taken?

A statement posted on the Pastebin website Tuesday suggests theaters that show the movie will face physical attacks and directly warns readers to stay away from them. It includes the line: “Remember the 11th of September...