The Segunda Division Group 1 side's small stadium is named after the local star striker who plays for Atletico Madrid.
Real have climbed to third in La Liga after a rocky start to the campaign, and they will expect to breeze into the next phase.
Manager Zinedine Zidane is likely to rotate his options, as he saves his superstars for the forthcoming trip to Tottenham Hotspur in the UEFA Champions League.
Here is how you can watch the cup game:
Date: Thursday, October 26
Time: 3:30 p.m ET/8:30 p.m. BST
TV: beIN Sports USA
Zidane will get the chance to play his younger players and fringe prospects in the cup, with Fuenlabrada expected to offer little resistance in front of a very small crowd.
Fuenla play their games in the metropolitan area of the capital city, and Real's second string should have no problems dispatching their opponents.
However, Zindane has watched his team huff and puff in the opening weeks of the season, and they have lacked motivation against much weaker sides than themselves.
Complacency has riddled the Spanish and European champions, but a defeat to Fuenlabrada would be a historic loss.
Despite their slow start this term, Real have won six from their first nine in La Liga, and results have started to improve.
Zidane challenged his team after their 3-0 win against Eibar in the league and declared his men are still not in top gear.
According to Marca (h/t the Press Association via Sky Sports), Zidane said:
"We did well in defence and I come away with the feeling that it was not all perfect, but satisfactory. It was important to get the three points today.
"Perhaps the fluency was lacking. We can be better, with the ball we can be better. In the end we made a lot of changes and sometimes you have to realise you cannot do everything perfectly."
Fuenlabrada lay second in their league and are in consistent form after winning seven of their 10 games this term.
The small team know this game represents one of the biggest days in their short history, and there is every chance Cristiano Ronaldo will be given the night off.
Ronaldo's potential absence could see Real lack fluency, but with a strong squad desperate for minutes, it should be a simple day at the office.