The former Chelsea frontman penned an 18-month contract with the Turkish outfit on Monday, but the Ivorian's former employers have insisted that they will report the transfer to FIFA.
In a statement on the club's official website, Shenhua said: "The club is deeply shocked. Drogba is still a Shanghai Shenhua Football Club member as the contract between the two parties is still within its period of validity.
"The Shanghai Shenhua Football Club is ready to gather evidence and submit the findings to FIFA in order to protect its interests."
Drogba moved to China from Chelsea at the end of last season.