The 18-year-old striker will stay with the Evo-Stik League Premier Division club for one month.
Spireites boss Paul Cook said: "It's important for young lads to go out and play football. They need to build up their football CV.
"If Jacob can go to Matlock and score some goals and make people speak about him in the right way it will only benefit him and the club."
Hazel has made three appearances for Chesterfield's first team this season.