No. The 1994 version was based off of Norse mythology, as the wearer of the mask became a reincarnation of Loki (yes, the same Loki from Thor/The Avengers fame, and a bonafide prankster) whereas the 1961 Mask was a psychological thriller/horror movie where the wearer of the mask was slowly driven insane. There is a fine line between becoming a prankster and committing murder, but the line exists, nonetheless.
However, in a larger context, the 1994 movie was based on the Dark Horse comic of the same name, which shared a closer storyline with the 1961 movie. The 1994 version was also intended to be a horror series, but the story was changed along the way. So, in some cases they are, in fact, related.