Alaa Bader al-Hashemi, 30, was executed at dawn after President Sheikh Khalifa bin Zayed al-Nahyan approved the death sentence against her, said the official WAM news agency, citing prosecutors.
The National, an English-language daily, said Hashemi had been put to death by firing squad.
Hashemi was sentenced to death last month for stabbing to death mother of three Ibolya Ryan, 47, in a toilet of an Abu Dhabi shopping mall on December 1, 2014.
The device failed to explode.
In the verdicts issued in June, the Federal Supreme Court in Abu Dhabi said Hashemi had used an Internet account to spread information that was likely to "jeopardise" the United Arab Emirates.
She was also found guilty of having sent funds to Al-Qaeda in Yemen, knowing that this money would be used for "terrorist acts".
UAE law allows for capital punishment but executions are rare and death sentences are usually commuted to life in prison.
Before his sentence was carried out, rights watchdog Amnesty International had reported last year that a dozen people had been executed in the UAE since 1997.
Hashemi was arrested 48 hours after the attacks in Abu Dhabi.
Security forces tracked her down using CCTV footage of her going into and out of the restroom where the murder occurred and near the doctor's building.
She was dressed in black from head-to-toe.
During her trial, Hashemi had asked the court to provide her with psychological help, saying she had "unreal visions" and would see "ghost-like people" due to a chronic mental illness.
