I take it you're referring to the amount of time Earth takes to revolve 360° on its axis. The period of time between a point on Earth directly facing the Sun is exactly 24 hours - our orbit accounts for the 4 minute discrepancy.

But I digress. There are two other definitions of 'day':

1. From Sunrise to Sunset
   Under this definition, the shortest 'day' is (at most latitudes) the Winter Solstice - Around the 22nd of December.
2. From one midnight to the next
   This is the interesting one. Consider the day in springtime when many people put their clocks forward to Daylight Savings time. That 'day' is only 23 hours between midnights. The shortest day in the year! Unfortunately Stef means the other one. :)