Local media reported that Lourdes Abejuela was taken to hospital after she was attacked by the lion, which escaped from its cage, but was at first discharged.
Quoting Abejuela's friend, papers said the domestic helper then suffered headaches, prompting her employer to take her back to hospital, where she died.
Reports said an investigation is ongoing to determine the Filipino woman's cause of death.
Sheikh Dr Sultan bin Mohammed Al Qasimi, Supreme Council Member and Ruler of Sharjah, issued the order.
Earlier this year, Dubai Police reportedly investigated a video that showed a lion in the boot of a four-wheel drive vehicle travelling along Sheikh Zayed Road in Dubai.
The nine-second clip on YouTube appeared to show a lioness in the Dubai-registered Nissan Armada.