According to a police statement, the attack occurred around 7.30 p.m. on Sunday at the shopping mall in Taikoo Shing, reports Efe news.
"Police strongly condemn violent acts and will conduct active and thorough investigation with a view to bringing offenders to justice, regardless of their motive and background," said the statement.
Local media reports have claimed the incident took place owing to political differences.
According to the South China Morning Post, the alleged attacker had a heated discussion over political issues outside the mall, after which he injured four people with a knife he had in his backpack.
Members of the public attacked him, also injuring a man who tried to protect him, and who was later arrested.
A district councillor reportedly had part of his ear bitten off.
Lawmaker James To Kun-sun told the South China Morning Post that witnesses heard the attacker shout "liberate Taiwan" and that it was believed to be a pre-meditated attack as he was carrying a knife with him.
The incident occurred during a new round of protests in Hong Kong in which 17 people were injured, according to data provided by the city's hospital authorities on Monday.
Hundreds of people on Sunday responded to an online call for a new unauthorized protest against alleged police brutality during demonstrations, as disgruntled citizens continue to demand an independent investigation.
Riot police were deployed in several shopping malls in the semi-autonomous city of China.
Several protesters caused damage at a metro station, others threw objects at policemen and trashed a restaurant, and others formed human chains.
The former British colony witnessed one of its most violent days on Saturday as clashes occurred between riot police and demonstrators.
The Hong Kong protests, which have been drawing massive crowds since June following a contentious proposed extradition law, have mutated into a movement that seeks to improve the democratic mechanisms that govern Hong Kong and safeguard the region's partial autonomy from Beijing.
However, some demonstrators have opted for more radical tactics than peaceful civil disobedience and violent clashes with the police have been frequent.
( With inputs from IANS )