The visitors, meanwhile, could reach the quarter-finals for the first time in 36 years.
Match preview
Frankfurt's impressive season continued on an upward trajectory by beating Hertha Berlin 3-0 in the Bundesliga on Saturday, with Randal Kolo Muani's brace making it four goals in three matches for the France forward.
Despite gaining the comfortable victory, Oliver Glasner's side remained outside of the top four by a point, but there remains plenty of time for them to make up that small margin across the coming months.
Moreover, with their first ever Champions League knockout tie against Napoli on the horizon later this month, Die Adler's season could yet be another magical one after lifting the Europa League last May.
A routine home win at Deutsche Bank Park against second tier opposition on Tuesday would set them up nicely ahead of a congested schedule, with Glasner hoping to help Frankfurt win their sixth DFB-Pokal in the club's history.
Darmstadt, meanwhile, will be hoping Tuesday's trip to Frankfurt is not the last time that they face Bundesliga opposition this year, with Torsten Lieberknecht's flying high at the top of the table in Germany's second tier.
Die Lilien's impressive 4-0 win away to SV Sandhausen on Friday night kept them two points clear of Hamburger SV at the summit, while opening up a healthy seven-point cushion ahead of third-placed Heidenheim, who currently occupy the promotion play-off spot.
Darmstadt missed out on achieving that position by goal difference only last season, with Hamburg squandering a one-goal lead from their first leg against Hertha, who turned things around in the second leg to remain in the Bundesliga.
While Lieberknecht will be determined for his players to prove that they belong at the top level when they arrive in Frankfurt in midweek, the 49-year-old will be realistic regarding his side's chances of progressing, while looking to ensure a possible defeat does not detract from their charge for promotion.
Eintracht Frankfurt DFB-Pokal form:
W
W
Eintracht Frankfurt form (all competitions):
W
D
W
D
D
W
SV Darmstadt 98 DFB-Pokal form:
W
W
SV Darmstadt 98 form (all competitions):
D
W
W
D
W
W
Team News
Frankfurt will remain without Eric Dina Ebimbe, whose ankle injury is likely to keep him sidelined until early April, while Faride Alidou and Jens Grahl are both doubts.
Glasner could look to rotate for this match, with the likes of Sebastian Rode, Kristijan Jakic and Rafael Santos Borre all likely to start after only appearing from the bench against Hertha at the weekend.
Darmstadt are likely to travel without Patric Pfeiffer, Matthias Bader, Klaus Gjasula and Aaron Seydel, who are all expected to remain sidelined for at least a few more weeks.
Lieberkecht may see no reason to change a winning team after dismantling Sandhausen in their last league match, especially with a five-day gap until their next fixture against his former club Eintracht Braunschweig.
Eintracht Frankfurt possible starting lineup:
Trapp; Tuta, Smolcic, Ndicka; Chandler, Rode, Jakic, Lenz; Knauff; Alario, Borre
SV Darmstadt 98 possible starting lineup:
Schuhen; Zimmermann, Muller, Isherwood; Ronstadt, Schnellhardt, Kempe, Holland; Vilhelmsson, Honsak; Tietz
We say: Eintracht Frankfurt 2-0 SV Darmstadt 98
Even with Glasner being likely to make several changes given that his side are competing on three fronts this season, Frankfurt should have too much quality for their opponents on Tuesday.
Darmstadt will not be short of confidence given their lofty position in the second tier - helped by their heavy victory on Friday - but they are likely to fall a little short against such high-calibre opposition.