McCartney set a national record of 4.82m in February and opened her European campaign with 4.75m in Rome last month, but has struggled since, no-heighting in Oslo and clearing only 4.20m in Stockholm.
The London Diamond League is the first meet she's had to withdraw from and McCartney is running out of chances to compete before the world championships in the same city on August 5-13.
"We need to be smart about it," she says. "I probably could compete now, but it wouldn't be worth it, if I'm not in good shape for the world champs."
Her next opportunity will come on July 22 at Heusden, Netherlands.
Meanwhile, middle distance exponent Nick Willis was due to open his European schedule over 1500 metres at Brussels on Sunday night (NZT).
Willis, the Rio Olympic bronze medallist last year, has just three races to achieve the 3min 36sec world championship qualifying standard, after shin splints delayed his competitive debut this season.