The pairing of the names of the two best men's clay-courters of the Open era provoked excitement within tennis, although 21-year-old Leo appears highly unlikely to have a career anything like that of his father Bjorn.
Ranked 461, Leo was given a wild card for the tournament in Bastad and competed well against his illustrious opponent before succumbing to a 6-3 6-4 defeat.
"Great feelings," said Nadal in his on-court interview.
"For me it has been a huge honour to play against the son of one of the biggest legends in the history of our sport.
"I think he played quite well, he has a future in front so I wish him all the very best."
Nadal was playing his first singles match since an opening-round loss to Alexander Zverev at the French Open in May.
The 38-year-old decided to stay on clay rather than risk further injury by switching to grass and has been practising with the goal of being at his best for the Paris Olympics later this month.
Nadal should have a stiffer test next against British number two Cameron Norrie, who defeated Jozef Kovalik in the first round on Monday.
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