The Rio Olympic bronze medallist cleared 4.20m but missed three attempts at 4.40m.
The 20-year-old was among the favourites in the nine-woman field. Her personal best of 4.82m was the third highest among the group.
Switzerland's Nicole Buchler won on countback from Sweden's Angelica Bengtsson with a vault of 4.65m. Venezuela's Robeilys Peinado was third, having also cleared that mark.
Neither Olympic champion Ekaterina Stefanidi of Greece nor Rio silver medallist American Sandi Morris competed.
McCartney bowed out at 4.55m in Oslo on Thursday, failing to clear the bar at any point.
She finished third with a jump of 4.75m at the Rome leg of the Diamond League on June 8.
Her prime target this year is the world championships in London in early August.
She has been based in Germany for the start of her northern hemisphere campaign, working at an athletics facility in Leverkusen. Pharmaceutical giant Bayer is based in the town and sponsors the venue.
McCartney is next scheduled to compete at the London Diamond League meet on July 9.
