The sentence was carried out on Monday morning after being approved by President HH Sheikh Khalifa bin Zayed Al Nahyan.
State news agency WAM said UAE Attorney General Ahmed Al Dhanhani confirmed the execution. Death penalties are carried out by firing squad.
Alaa Al Hashemi was found guilty last month of stabbing Ryan to death in a toilet cubicle on December 1, 2014.
Al Hashemi was dubbed the ‘Reem Ghost‘ because footage from the scene showed her calmly leaving the mall in a niqab and abaya.
Ryan was shopping when she was stabbed to death in the toilets of the Reem Island shopping centre in December 2014.
Prosecutors earlier said Ryan was targeted because she spoke with an American accent.
Al Hashemi, 30, was also convicted of planting a bomb outside the home of an Egyptian-American doctor at a tower on the Corniche. It was found by the doctor’s young son but failed to go off.
Al Hashemi was also convicted of sending money to Al Qaeda in Yemen, in the knowledge it would be used for terrorist acts.
A further charge said the woman had used an online account to spread information that ridiculed and harmed the UAE.