The accident took place during technical rehearsals for the Andrew Lloyd Webber-Tim Rice musical, in which Lee Mead stars in the title role after winning the BBC reality show "Any Dream Will Do."
The Sun reported that the two performers were injured by a moving staircase. A source told the paper, "There is a lot of mechanical scenery, and the cast have to get out of the way. But two people didn't move quickly enough and had their feet crushed."
The show's spokesperson said that neither actor was seriously injured and that both have returned to the production following treatment.
The incident follows a more serious accident during one of the preview performances of Lord of the Rings, when actor Adam Slater had his leg trapped in a section of the fast-moving hydraulic stage.
That accident resulted in the show closing for two days. The revival of Joseph is due to open at the Adelphi on July 17, following previews that begin July 6.