Nadal, the top seed in the event in the absence of injured world number one Carlos Alcaraz, had opened by losing his first two matches in the Green Group. He was already eliminated when he faced Ruud, who won his first two matches to book a semi-final spot.
World number one Carlos Alcaraz retired injured against Holger Rune at the Paris Masters on Friday, sending his fellow 19-year-old through to the semi-finals.
Spanish teenager Alcaraz, hoping to win a third Masters title of the year after previous successes in Miami and Madrid, saw off former world number three Dimitrov 6-1, 6-3 in 72 minutes.