There are several possible explanations. One is the dawn phenomenon. This is believed to be due to the release of growth hormone overnight, so that someone with a normal or slightly high blood gluose at bedtime has a rise in the blood gluose level while sleeping. Best way to avoid is to add an insulin that works overnight: either long-acting  Lantus, or a bedtime shot of NPH.

There is a second reason for early-morning high sugar levels: the so-called Somogyi effect, nowadays usually called rebound. The sequence of events is as follows: excess insulin or evening exercise results in nocturnal hypoglycemia; then the low sugar stimulates counter-regulatory hormones such as epinephrine, growth hormone, cortisol, and glucagon, which force the blood sugar upwards. Sadly, the sugar doesn't level off, but continues upwards to high levels. How to avoid? Well, if you take Regular or short-acting analog insulins (Humalog/Novolog/Apidra) at bedtime, you're inviting a nighttime hypo and subsequent rebound. Or if you're on a big dose of NPH at suppertime (its peak effect being while you're sleeping). Of if you do heavy exercise in the evening and don't compensate with a bedtime snack with protein.

How to tell them apart? Best way is continuous blood glucose monitoring overnight; slightly easier is setting an alarm clock and checking blood gluoses at 3 am. The key is whether your blood glucose in the middle of the night goes low or not.

The story I like best about why there's a dawn phenomenon (although it's clearly apocryphal) is that we were designed that way so farmers would have enough energy on-board to go out and do their early morning chores without stopping to eat breakfast first.