The action against Alexandre Benalla was taken after "new facts" emerged in the case, French President Emmanuel Macron's office said on Friday.
Benalla was suspended hours after the video was shared by local news outlets.
"This sanction was to punish unacceptable behaviour and it was a final warning before being sacked", said the president's spokesman, Bruni Roger-Petit.
In the video, a man wearing a police helmet and identification tag was shown dragging a woman away and then beating a demonstrator on May 1.
Before he joined the presidential staff he had the role of head of security during Mr Macron's election campaign in 2017. The riot police close by appeared to let Benalla carry out the violence.
Amid the outcry Thursday, the French public prosecutor opened an inquiry into the Benalla case, an investigation that could ultimately lead to charges against him, as well as further embarrassment to the Elysee Palace.
On a trip to southwestern France on Thursday, Macron declined to answer questions from reporters on the subject, saying only in a video posted by a Le Figaro reporter: "I didn't come here to see you".
Several opposition leaders voiced criticism over Benalla's punishment, arguing it was too lenient.
The man is heard begging him to stop, with officers at the scene not intervening.
Benalla, who has previously worked as bodyguard, is not a policeman but had been given permission to "observe police operations" during a day-off for the May 1 public holiday, said presidential palace spokesman Bruno Roger-Petit.
"He is suspected of receiving material from the police he was not authorized to have", the Elysee said.
Interior Minister G-rard Collomb "strongly condemns these actions which, if they are confirmed, constitute a serious breach of ethics and undermine the exemplary image which must, in all circumstances, characterize the action of the national police", the statement said.
Supporters of Macron claimed that the punishment handed down to Benalla - suspension without pay for two weeks and a transfer to an administrative job - was appropriate.
The attempt at damage control follows an outcry by Macron's critics, not least because the 40-year-old former investment banker won the presidency with pledges to restore transparency and integrity to the nation's highest office.
"By not immediately managing a disciplinary problem, Emmanuel Macron now faces a political crisis", wrote the right-wing Le Figaro daily - which usually makes no secret of its admiration for the president.
"As a result. the presidency has chose to start Alexandre Benalla's dismissal procedure", the official added.
Labour unions hold demonstrations every year on May 1 in France and clashes with police are not uncommon.
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