Sleep off
Definition 1 of 1
Pro Tip 1/3Colloquial Usage
The phrase is casual and used more in spoken or informal contexts than in formal writing. 
I'll just sleep off this tiredness and then call you.
Pro Tip 2/3Recovery Focus
Emphasizes intention to overcome discomfort or illness by sleeping. 
She decided to sleep off the flu symptoms instead of going out.
Pro Tip 3/3Not Instant
Indicates the process of recovery will take some time, usually several hours of sleep. 
He's going to need to sleep off that jet lag before we meet.