Alaa Bader Abdullah is accused of stabbing to death teacher Ibolya Ryan, 47, in a shopping mall restroom and attempting to murder another American, a doctor of Egyptian origin, by planting a bomb outside his apartment.
The jihadist-inspired attacks took place within hours of each other in the UAE capital on December 1.
The suspect was tracked down and arrested after CCTV footage was released of her dressed in black from head to toe going in and out of the restroom where the teacher's murder took place.
Abdullah was also alleged to have collected explosive materials and created an Internet account to promote the "ideas of a terrorist group".
Investigators found she had "listened to lectures by late Al-Qaeda leaders Osama bin Laden and Abu Musab al-Zarqawi, watched video clips of killings and beheadings," among other similar activities, said Kubaish.
She was said to have "embraced takfiri and jihadist ideology and then engaged in terrorist acts in support of the terrorist organisations Al-Qaeda and Daesh," he said in reference to the Islamic State (IS) group.
Abdullah has been referred to the Federal Supreme Court to face the charges, he said without giving a date for the start of the trial.
The United Arab Emirates in September joined the US-led coalition carrying out air strikes against IS in Iraq and Syria.
Last year, it issued a list of 83 Islamist groups which it classified as "terrorist organisations".
Violent crime is relatively rare in the UAE although there have been attacks on foreigners elsewhere in the region.
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