In her opening leg of the Diamond League in Rome on June 8, McCartney finished third with a jump of 4.75m.
The injury is understood to be a niggle, rather than a tear. She is to have an MRI scan in Cologne, Germany, 35km from the base she and McColl have at Leverkusen.
McCartney, 20, has the world championships in London starting on August 5 as her priority this year.
There is no women's pole vault at the next two Diamond League meets, in Paris on July 1 and Lausanne five days later, but it is on the programme for the London event on July 9.
McCartney is due to line up there in what would be the final opportunity for the best leapers to compete in a high-class field before the world champs, although there are other lower-key competitions which would provide possible warm-up meets.