The films, which were originally slated for release on 27th March and 10th April respectively, have now been postponed - and there is no word yet on alternative release dates.
The studio said in a statement that the decision was made out of an "abundance of caution", adding that "we truly believe in the moviegoing experience, and we are looking at new potential 2020 release dates to be announced at a later date.”
The news will come as a particular blow for X-Men spin-off The New Mutants, which has already faced long delays in reaching the big screen.
The film, which stars Maisie Williams and Anya Taylor-Joy, was originally set for release back in 2018, but assorted setbacks have caused it to be repeatedly postponed.
Meanwhile Niki Caro, director of Mulan – the live action adaptation of the beloved 1998 animated film – remained positive, saying in a statement she "can't wait for the day where we will all get to experience this tale of a girl warrior who became a legend together."
She added, "Making this film has been one of the most satisfying and exhilarating experiences of my entire career, and I've been so fortunate to be on this journey with some of the best cast and crew in the business – people who truly embody the attributes of Loyal, Brave, and True.
"We are so excited to share this film with the world, but given the current ever-shifting circumstances were are all experiencing, unfortunately, we have to postpone the worldwide release of Mulan for now.
"Our hearts are with everyone the world over who is affected by this virus, and we hope that Mulan's fighting spirit will continue to inspire those who are working so hard to keep us all safe."
The European premiere of the film had been scaled back earlier in the week as fears around the virus mounted.
Mulan and The New Mutants join a list of movies affected by the virus, including blockbusters No Time To Die, Peter Rabbit 2, A Quiet Place: Part II and Fast and Furious 9 all now delayed.