It's not correct, but not because of the "the."
I slept all day. I slept all night. I worked all afternoon. I did my taxes all morning. When we use "all" with a part of the day, we don't use "the."
The problem is that "to wake" is an action that happens in an instant. You don't "wake" all night.
I was awake all night.
I kept waking up over and over, all night.
I woke up repeatedly throughout the night.
But not: I woke all night.