According to Snopes (snopes.com), it is not. As in, there is not a specific day that is the most depressing day of the year.
That said, if you read carefully, you can see why people accept this notion. January can be a difficult month for many reasons. You might feel that the entire month is filled with Blue Mondays. Take it easy on yourself, especially if you have challenging resolutions you are trying to complete.
Good luck. Stay healthy.
(Image, via The Sun, shows the so called formula for calculating Blue Monday)