In a foreign land in the grip of a pandemic, the two young women kept to themselves in public.

But what was to have been a simple grocery run turned into a nightmare for the undergraduates - one Singaporean and one Malaysian - who were verbally abused and physically assaulted in the heart of Melbourne in the Australian state of Victoria last Wednesday.

A video circulating on social media shows the 18-year-old Singaporean and her 20-year-old friend being attacked.

The incident, believed to be racially motivated, has drawn strong criticism from the Australian authorities.

Victoria Police said the victims were walking along Elizabeth Street near Queen Victoria Market at about 5.30pm when the two perpetrators began verbally abusing and assaulting them. The area is in the city's central business district.

Describing the attackers as skinny Caucasians, the police said they reportedly shouted "coronavirus" repeatedly and hurled death threats at the students.

Melbourne's Nine News reported that the students were also told to "go back to China" and they were attacked when they responded to the taunts.

The 20-second video shows a woman in a sleeveless parka and white skirt grabbing one student by the hair and punching her repeatedly on the head before dragging her to the ground and kicking her.

The attacker's accomplice, in a pink jacket, pushes the other student, then blocks her and another woman from helping the first victim.

The assault stops after a man intervenes by shouting at the assailants.

The incident was reported to the police, who said the victims suffered minor injuries.

The injured women, whose faces were blurred out, later told Nine News they are now terrified to leave their homes.

One of them said the attacker told them: "Get the f*** out of our country - you don't belong here."

Her friend added, while sobbing: "I'm really scared they think it's okay to do (this) to other people."

Identifying the victims as undergraduates at the nearby University of Melbourne, vice-chancellor Duncan Maskell condemned the attack, saying: "This is a disgusting and unprovoked attack on two of our female students.

"These senseless and vicious attacks on two young women must never be tolerated in our community. The people who did this are a disgrace."

Calling it a racist attack, the university's student union president Hannah Buchan said the undergraduates were told by the attackers to "get out of our country".

Melbourne Mayor Sally Capp also condemned the attack on social media, saying: "I am appalled by the disgraceful attack on two young students... The violence displayed is completely unacceptable. It does not reflect the values that Melburnians stand for or the behaviour we expect in our city."

During the assault, one of the victim's AirPods earphones fell off and were stolen by a man who was not involved in the attack.

Described as a 1.75m-tall Caucasian with a solid build, he was wearing a black puffer jacket and carrying a black backpack.

In a statement on Sunday, Victoria Police said they have charged a 21-year-old Melbourne woman in relation to the case.

Jakkara Brigham appeared before the Melbourne Magistrates' Court yesterday and was charged with recklessly causing injury and committing the offence while on bail.

Investigators are trying to identify the second woman involved in the assault and a man who was allegedly with them but is not seen in the video.

In February, a 23-year-old Singaporean student was assaulted in London in an attack that was also believed to be racially motivated. He posted a photo of himself with a swollen eye after the attack.

The Ministry of Foreign Affairs said in a statement yesterday evening that it is aware of the latest incident, and the Singapore High Commission in Canberra is in touch with the Singaporean student to give consular assistance.

The High Commission is also reaching out to the local authorities to ensure the incident is investigated and dealt with according to the law, the ministry added.

The ministry also said it has approached the Australian High Commission in Singapore, which has stressed the Australian authorities are taking the incident very seriously and investigations are under way.