Alaa Bader al-Hashemi is on trial at the Federal Supreme Court on charges of stabbing to death teacher Ibolya Ryan, 47.
She is also accused of attempting to murder an American doctor of Egyptian origin by planting a bomb outside his apartment.
The attacks took place within hours of each other in the UAE capital on December 1. Hashemi was arrested less than 48 hours later.
"The court decided to refer the accused to a specialised medical centre" to assess her "mental condition", the official WAM news agency said.
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International media have been denied access to her trial, which began on March 23.
The authorities say Hashemi embraced "jihadist ideology and then engaged in terrorist acts in support of the terrorist organisations" -- Al-Qaeda and the Islamic State group.
She has also been charged with collecting explosive materials as well as financing and promoting the ideas of "terrorist" groups in the United Arab Emirates.
The next hearing in her trial was set for April 27.