A dramatic arrest on a narrow Sydney street has been caught on CCTV, showing a stolen luxury sports car allegedly ram police vehicles and  injure two officers.

Police allege the silver Mercedes AMG is linked to violent robberies, one of which allegedly involved a sword, carried out over the past two weeks in the CBD.

Dramatic scenes unfolded about 5.30pm on Wednesday when the car was stopped in Alexandria by two unmarked police cars that approached it from both sides.

The luxury car, which was carrying four young people, allegedly reversed into one of the police vehicles and injured a female officer, before accelerating into the other police cars.

A Dog Unit vehicle that arrived at the scene was also hit and a male officer sustained lacerations to his arms and legs.

The injured female officer spent the night at Royal Prince Alfred Hospital with a minor laceration to her head, New South Wales Police said on Thursday.

Paramedics treated the male officer at the scene.

A man and three teenage boys were arrested at the scene.

The 22-year-old man was taken to Redfern Police Station where he was charged with armed robbery with offensive weapon, use offensive weapon in company to prevent detention, take and drive conveyance without consent of owner, drive manner dangerous, never licensed person drive vehicle on road, resist officer in execution of duty, and possess prohibited drug.

He was refused bail and was due to appear at Central Local Court on Thursday.

The teenage boys aged 16, 16 and 17 were taken to Newtown Police Station.

The 16-year-old boy was charged with armed robbery, take and drive conveyance without consent of owner, resist officer in execution of duty, and breach of bail.

The second 16-year-old boy was charged with armed robbery, take and drive conveyance without consent of owner, resist officer in execution of duty, and aggravated break, enter and steal.

The 17-year-old boy was charged with take and drive conveyance without consent of owner, and two counts of aggravated break, enter and steal.

The teenagers were refused bail and were due to appear at Children’s Court on Thursday.

Police allege the silver AMG is connected to robberies in Sydney over recent weeks.

A woman was walking along Mountain Street in Ultimo about 6.45am on Monday last week when two males wearing hooded jackets approached her.

It’s alleged the pair assaulted the woman while attempting to steal her handbag and driving away from the scene.

A short time later, police said a silver Mercedes AMG approached a woman who was standing on Bulwara Road in Pyrmont.

The woman said her bag, which contained a laptop and iPad, was taken.

Just after 4am this Monday, police said a man was walking along Quay Street in Haymarket looking at his mobile phone when he was allegedly punched in the side and back of the head.

The man was allegedly kicked and punched by four males while he lay on the ground, before one of the men produced a sword and took the man’s mobile phone.

-with AAP