The big Serb defender flew to Los Angeles with the rest of the Chelsea squad on Sunday for the second leg of the pre-season tour despite the injury, and will have treatment in the USA.
But Ivanovic is now expected to be out for three weeks, which would put his pre season preparations for the new campaign well behind schedule, and could mean he misses the opening game of the season against West Ham on August 15.
Ivanovic, 32, picked up the injury in Chelsea’s 3-0 friendly win over RZ Pellets in Austria on Wednesday.
Chelsea, meanwhile, have enquired about Lazio’s Dutch international defender Stefan de Vrij, who could cost them around £15 million.
Blues manager Antonio Conte has grown tired of the prolonged negotiations for Napoli centre back Kalidou Koulibaly who the Italian club are asking for more than £45m for.
The highly rated de Vrij would be a much cheaper option, especially with the cash-strapped Rome club much more keen to sell.
Conte though still has Roma defender Kostas Manolas high on his wish list, as well as Benfica’s Swedish youngster Victor Lindelof.