A teenager has been charged with stabbing a woman at a shopping centre in south-east Melbourne today.

Police said a 25-year-old woman was on her way to work and was inside M-City Shopping Centre on Blackburn Road, Clayton, about 7:30am when a male she did not know stabbed her.

She is in a serious but stable condition in hospital.

A passer-by came to her aid and called Triple Zero (000).

Police were told the offender ran from the shopping centre.

Two people walk outside the glass exterior of a multi-storey building that has a "Woolworths" and a "K Mart" sign on it.

Police said the offender fled from the shopping centre after the stabbing. (ABC News: Natasha Schapova)

Officers arrested a 16-year-old boy at a medical centre in Clayton soon after.

He has been charged with a number of offences including intentionally causing injury, assault with weapon, theft and committing an offence while on bail.

He was remanded in custody to appear at a children’s court at a later date.

Some workers in the centre received an email from centre management informing them of the incident, advising them additional security would be brought in as a precaution and that there would be more police patrols in the centre.

Anyone who saw the stabbing or has information is urged to contact Crime Stoppers on 1800 333 000 or www.crimestoppers.vic.com.au.