Nilsson cleared 1.93 meters on the first attempt, which gave a medal. But when the bar was raised to 1.95, it became three failed attempts for the Swede. Her personal best is 1.94 meters, which she set at the end of June.
The gold went to the Serbian Angelina Topić, who cleared 1.95 meters on the second attempt.
Joana Herrmann, Germany, took the bronze on 1.91 meters.
Previously, Sweden has a medal, a silver, from this year's U23 European Championship.
It was taken by Jonathan Grahn on 10,000 meters. He also ran the men's 5,000 meters on Saturday, when it became a sixth place.