A man has been arrested after allegedly stabbing a stranger on a bus in broad daylight in Sydney's inner city on Saturday.

Police say a 34-year-old man was travelling on a bus on Flinders Street in Darlinghurst around midday when he was suddenly stabbed by another passenger.

The alleged attacker – 19-year-old Trekieye Williams – then exited the bus and ran from the scene.

The injured man was taken to St Vincent's Hospital with non-life threatening injuries to his left hand, arm and chin.

Following a short manhunt, officers arrested the 19-year-old in Surry Hills.

Police say earlier that day, Mr Williams had also assaulted and robbed another man in Bondi.

He's been charged with seven offences in total including intent to cause grievous bodily harm and aggravated robbery.

Mr Williams has been denied bail and will appear at Parramatta Court on Sunday.