The Norwegian ousted Taylor Fritz to reach the quarter-finals and secured his first win against the Russian in their fourth meeting.
Strong on clay, Ruud only converted two of his eight break points but it was enough to secure victory, with Medvedev, who dislikes the surface, not producing a single break.
Ruud put heavy pressure on Medvedev's serve in the first set, breaking in the fourth game and serving it out.
The second set featured just a single break point, earned and converted by Ruud in the 11th game, enabling him to serve for the match.
Medvedev made 33 unforced errors and committed four double faults on a disappointing afternoon for the world number 10.
Ruud, ranked 15th, will face Francisco Cerundolo in the final four after he edged past Jakub Mensik 3-6, 7-6(5), 6-2.
Fifth seed Jack Draper swept past Matteo Arnaldi 6-0, 6-4. He awaits the winner of the other quarter-final between Lorenzo Musetti and Gabriel Diallo.