Turkey's President said allied Syrian forces had taken "total" control of the town, which was previously controlled by the Kurdish militia known as the People's Defence Units or YPG.
The statue was of the blacksmith Kawa, a central figure in a Kurdish legend about the new year celebration of Nawroz.
"Afrin city center is under control as of 8:30 this morning", Turkish President Tayyip Erdogan told a rally commemorating the World War One Gallipoli campaign, adding that Turkish and Free Syrian Army flags had been raised in the town center.
The Turkish assault on Afrin, named Operation Olive Branch, began on 20 January, with the aim of ridding the city and surrounding region of the YPG.
Committee member Rojeen Qaqu said the demonstration "highlighted the worsening humanitarian situation and grave danger of further loss of life in Afrin City".
The YPG denies any direct organisational links to the PKK - an assertion backed by the USA, which is allied with the YPG in the battle against the jihadist group Islamic State (IS) in Syria. He said there were still armed fighters when he left the town who had vowed to keep up the fight.
The seizure of Afrin, a mainly Kurdish city near the Turkish border, came as other Syrian rebel groups appeared close to collapse in the besieged area of eastern Ghouta, in the suburbs of Damascus.More news: Pakistan not to attend WTO meet starting today
Activists say 280 civilians have died, although this is denied by Ankara.
The Britain-based Syrian Observatory for Human Rights said almost 200,000 people fled the Afrin region in recent days amid heavy air strikes, entering Syrian government-held territory nearby. "There would be resistance pockets in the city and there are undoubtedly many improvised explosive devices and booby traps lying around", said security expert Abdullah Agar on NTV news channel.
On Sunday, Kurdish officials said they had evacuated Afrin of civilians.
A Turkish victory in Afrin could push the U.S.to ensure that Kurdish fighters withdraw from the town of Manbij to the east of the Euphrates River, Agar noted.
Government spokesman Bekir Bozdag said the military campaign would continue to secure areas around Afrin and make sure food and medicine were available. "But terror and terrorists in Afrin are over", he said.
However, in a televised statement, the co-chair of the Afrin executive council, Othman Sheikh Issa, said the war against Turkey had entered "a new stage". But a growing number of witness accounts and social media posts indicated that the Free Syrian Army had entered. Erdogan has said the people of Afrin will return.
Turkey also fears the establishment of a Kurdish self-ruled zone in Syria that could inspire its own Kurdish minority to press for greater autonomy.
Turkey launched an earlier cross-border operation in 2016 to clear an area in northern Syria of IS and the YPG, preventing the Kurdish group from linking Afrin with the much larger territories it holds to the east.