The suspect was wearing the traditional black robe, full-face veil and gloves commonly worn by local women throughout the Arab Gulf region, local police said.
A statement posted on the Abu Dhabi Interior Ministry’s website said the victim was stabbed with a sharp tool that has been confiscated by police.
The statement said the American woman was 37 years old. Her name has not been made public.
The victim had 11 year-old twins who are now in the custody of police until their father, who is the victim’s ex-husband, arrives from abroad.
Col Rashid Borshid, head of the criminal investigation department, said the attacker remains at large. He said police are investigating possible motives and the gender of the attacker.
He said a fight broke out between the victim and the attacker in the women’s restroom just before the stabbing, which took place on the upscale Reem Island in Abu Dhabi. “Police will spare no effort in order to unveil this heinous crime and bring the culprit to justice,” he was quoted as saying in the statement.
The US Embassy in the United Arab Emirates said they are aware of the incident that took place and are in contact with Emirati authorities. The embassy said it stands ready to offer all possible consular services.
The UAE is a Western-allied, seven-state federation that includes the glitzy commercial hub of Dubai and the oil-rich capital of Abu Dhabi. It is home to a sizable Western population where foreigners outnumber Emirati citizens.
The UAE prides itself on being a safe haven in the turbulent Middle East. It is part of the US-led coalition conducting air strikes against Islamic State group fighters in Iraq and Syria.
Iran has launched air strikes against Islamic State (IS) militants in eastern Iraq, the Pentagon has said.
Pentagon spokesman Rear Admiral John Kirby said the US believes it may be the first time Tehran has launched manned aircraft from inside Iran to strike targets in Iraq.
The US had not co-ordinated air strikes or military activities with Iran, he said, adding that America continued to fly missions over Iraq and it was up to the Iraqi government to avoid conflicts in its own airspace.
Iranian military leaders have acknowledged that dozens of their forces have been in Iraq fighting alongside Kurdish troops battling the extremists. The US has not invited Iran to join the coalition fighting IS and Iran has said it would not join in any case.
A woman detained in Lebanon is not a wife of Islamic State leader Abu Bakr al-Baghdadi, according to an Iraqi official.
The denial comes the day after Lebanese authorities said they were holding a woman believed to be one of al-Baghdadi’s wives.
They said she was detained for travelling with a fake ID and she had claimed to be the reclusive extremist leader’s spouse.
Iraq’s Interior Ministry said the woman is Saja Abdul Hamid al-Dulaimi, an Iraqi national who travelled to Syria before arriving in Lebanon.
Spokesman Saad Maan Ibrahim said she is the sister of Omar Abdul Hamid al-Dulaimi, who is held in Iraq as a terror suspect.
Mr Ibrahim said al-Baghdadi has two wives but neither is named Saja al-Dulaimi.