Liu is fluent in English, after she lived in New York when she was younger. She began in television before appearing in 2008's The Forbidden Kingdom, which starred Jet Li and Jackie Chan.
Tan said: "What is more important is that previously Chinese actors in Western movies played non-essential roles, but this time Liu will play the leading role."
Hollywood has faced a string of accusations of "whitewashing" in recent years.
Many Chinese filmgoers were angry last year when Matt Damon was cast in the lead role for The Great Wall, which was set in ancient China.
Constance Wu, a Taiwanese-American actress, said ahead of the film's release: "We have to stop perpetuating the racist myth that only a white man can save the world."
The casting of Scarlett Johannson in Ghost in the Shell, Hollywood's remake of the Japanese anime of the same name, also provoked a storm of criticism, while Emma Stone's role as Allison Ng in Aloha sparked anger as did Tilda Swinton's casting in Doctor Strange as The Ancient One, originally a Tibetan monk in the Marvel comics.
Ed Skrein, a British actor, turned down the role of Major Ben Daimio in a new Hellboy film earlier this year because the character is of Asian heritage.
The news that Liu has been cast as the lead role in Mulan also triggered jubilation on Chinese social media.
"I am so happy, I am going to explode," said one comment. "She is the first Chinese Hollywood Princess."
However, Quartzy, a lifestyle website, says Liu is one of China's worst actresses.
It said that on Douban, a leading Chinese film forum, Liu currently holds an average rating of 5.2 out of 10 for more than 20 films in which she has starred.
Mulan will be directed by Niki Caro and is expected to be released in 2019.