The petition highlights fears that the area could be redeveloped. Birmingham City Council has been invited to comment.
Earlier this month it was announced that the Crown Pub, also on Station Street and the venue where Birmingham rockers Black Sabbath played their first gig, would not reopen after catering plans collapsed.
Mr Street said he was aware of development issues and had written to the Government to ask if Crown could achieve listed status.
He described Station Street as “just the tip of the iceberg” and said: “The closure of The Electric Cinema is a lightning rod for people’s deep concerns about the future.”
Ian Francis, who runs the Flatpack Film Festival, an annual festival that plays at venues across the city, said he knew The Electric’s lease was up for renewal.