The Nailers travel to Causeway Lane for a first qualifying round tie against their Evo-Stik League rivals from a division above them.
While Belper's search for a first league win continued in midweek with a 1-1 draw at home to Leek Town, Matlock wrapped up an early double against Frickley Athletic with a 3-1 victory.
The Nailers could include as many as four former Gladiators in midfielders Steve Warne, Colin Marrison and Simon Harrison, plus winger Ryan Mallon.
"Being drawn against Matlock adds a bit of extra spice," said Belper boss Peter Duffield. "It's a massive game for both clubs.
"Both sides will be desperate to win, for financial reasons and for bragging rights, especially with us having a few ex-Matlock players."
Duffield's opposite number, Mark Atkins, added: "It'll be a tough game, what with the old players coming back and the fact it's a local derby but we're looking forward to it and, hopefully, we'll be strong enough to go through."
Belper once again had to come from behind to earn a point against Leek, following last Saturday's 3-2 defeat by Market Drayton Town.
"We were disappointed on Saturday as we didn't think we deserved to lose," said Duffield.
"Tuesday was probably our best performance of the season and we dominated for large periods.
"Again, the lads showed great spirit to come back but we just can't seem to get in front at the moment."
This is Derbyshire