Saudi authorities have arrested someone for filming the incident, said local newspaper websites, including Okaz and Al-Riyadh, in reports accompanied by still shots from the recording.
They did not say what the arrest was for.
The official Saudi Press Agency said Monday that Layla bint Abdul Mutaleb Bassim was executed in the Muslim holy city of Mecca for killing her husband's six-year-old daughter.
"Investigations led to her trial which proved she was guilty," the interior ministry said, quoted by SPA.
The child, also "Burmese," died from a beating and from being raped with a broomstick, it said.
"I did not kill. There is no God but God. I did not kill," cries the woman, covered in black, apparently kneeling on the pavement circled by police officers in the video on LiveLeak.
"Haram. Haram. Haram. Haram. I did not kill ... I do not forgive you ... This is an injustice," she screams in Arabic, using the Islamic term for something that is forbidden.
The executioner, dressed in a white robe, forces her to lie down on the ground, near a pedestrian crossing. Mountains are seen in the distance.
"I did not," she continues before a final scream as the executioner's curved sword severs her head, in a traditional execution for the kingdom, which carries out death sentences in public.
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A voice then reads out her crime.
Many Twitter users protested the video being circulated on the Internet because it could be seen by the woman's family, but did not object to the beheading itself.
Several other videos purportedly showing beheadings in Saudi Arabia have circulated online over the past three years.
Bassim was one of 10 people beheaded so far this year under the kingdom's strict version of Islamic sharia law.
Saudi Arabia executed 87 people last year, up from 78 in 2013, according to an AFP tally.
A United Nations special rapporteur has said trials leading to the death penalty in Saudi Arabia are "grossly unfair".posted
The kingdom had the third-highest number of recorded executions in 2013, behind Iran and Iraq, Amnesty International says.
Rape, murder, apostasy, armed robbery and drug trafficking are punishable by death in the oil-rich Gulf state that is a close ally of Washington.
Saudi authorities identified Bassim as holding "Burmese nationality", using the former name for Myanmar, but did not specify if she was from its Rohingya Muslim community.
Myanmar's embassy said that without seeing her passport, it could not confirm whether or not she was a citizen.