The petition, which has collected more than 4,000 signatures since launching via Care2 till March 18, has asked Warner Bros to "stop casting white actors to play people of color!", reported Us magazine.
"This casting choice is particularly shameful for a children's movie. Telling children their role models must be all white is unacceptable," the petition read.
Hugh Jackman will play Black Beard while Garrett Hedlund has been cast in the role of Captain Hook.
The film is slated to release in July 17, 2015.