Isinbayeva, Olympic champion in 2004 and 2008, had been due to return to competition for the first time since the birth of her daughter in June 2014.
"I really hate to disappoint people but today when I was warming up I felt a sharp pain while making a jump and I understood that if I continued to jump I could tear a muscle," Isinbayeva, 33, told the All Sport news agency.
"It's an old injury in my Achilles tendon in my lead-off leg," she added.
The Russian, who won gold at the Moscow world championships in her last appearance in August 2013, said she would now head to Munich for a scan.
Isinbayeva's chances of competing in the Rio de Janeiro Olympics in August were hit when Russia was suspended from world athletics last November following allegations of widespread and state-sponsored doping in a report by the World Anti-Doping Agency (WADA).
The new head of Russia's Athletics Federation Dmitry Shlyakhtin said after his election last month that his top priority was to get the country's athletes to the Rio Games.
(Reporting By Dmitriy Rogovitskiy; editing by Clare Fallon)
