Jabeur dismissed ninth-seeded Jelena Ostapenko 6-0, 6-4 to reach the last eight along with top seed Iga Swiatek who eased past home favourite Sara Sorribes Tormo 6-1, 6-0.
But Jabeur, the 2022 Madrid champion, later took a swipe at tournament organisers, telling reporters she believes tennis still has a way to go to achieve gender equality, despite it being the leader in women's sport.
"Definitely tennis is a sport that I'm proud to play in as a woman," said the world number nine, who next plays either Coco Gauff or Madison Keys for a place in the semi-finals.
"But I feel like we have a long way, especially here in Madrid and in Rome, in Europe in general. I feel like they need to respect women more and they need to respect how we are playing."
Sharing examples from her personal experiences at events, Jabeur said women players were not given the same access to practice courts as the men, and noted how WTA matches were not shown on TV as frequently as ATP matches.
"The way they treat women here and men, they're completely different. Maybe people from outside, they don't see it. I'm definitely one of the people that I want to speak up," she added.
"Here in Spain, I would love to go to the hotel and open the TV and see a woman's tennis match.
"I haven't seen once one tennis match of a woman. Obviously, I understand there are a lot of Spanish (male players) playing, but asking for one match? Even the female Spanish (players) they are not even showing.
"For me it's really frustrating to see that. How can you inspire young girls without showing any match in that?"
Meanwhile, Swiatek dropped her opening game before sweeping the next 12 against her Spanish opponent to book a quarter-final meeting with Brazilian left-hander Beatriz Haddad Maia.
"We played many tough matches against each other so it's not going to be easy," said the Polish world number one of her upcoming opponent.
"She's always a very intense player and knows how to play on clay."
In the men's competition, American Ben Shelton saw his unbeaten 5-0 start to the clay season come to an end at the hands of Kazakhstan's Alexander Bublik, who won 3-6, 7-6 (7/2), 6-4 to reach the fourth round, where he awaits Daniil Medvedev or Sebastian Korda.
