The big spending Chinese club's owner revealed the Ivorian is unlikely to arrive in time to adequately prepare for the July 14 clash, delaying his maiden appearance.
The 34-year-old Ivory Coast striker had been expected to arrive in time to debut against rivals Beijing Guoan in the Chinese Super League on July 14.
However, owner Zhu Jun admitted the former Chelsea man would likely arrive in Shanghai on July 13 or 14 at the earliest, which wouldn't be adequate preparation for the game.
Speaking to the Oriental Sports Daily, Zhu was asked whether Drogba would miss the Guoan clash and responded: "Yes, from the current situation."
He explained: "But if there is no Drogba, we also have our own tactics... But it doesn't matter, we won't let ourselves down."
Shenhua's following game after that would be away to Yakubu Aiyegbeni's new club Guangzhou Fuli on July 22.
Meanwhile, Beijing Guoan's new big name signing Frederic Kanoute is poised to make his debut in the clash with Shenhua.
Former African Footballer of the Year Kanoute's move to Guoan was confirmed late last month after he left Sevilla.