Christmas shoppers reportedly fled the North Yorkshire store when screams and shouting was heard in the moments after the attack.
One witnesses recalled how brave employees 'pinned' the suspect down on the ground before he was initially arrested by police/
The police confirmed the suspect 'was initially detained by brave members of staff and public, before he was arrested by officers who were quickly on scene'.
He has since been arrested on suspicion of murder following the woman's death.
The police further added, 'He was taken into custody on suspicion of attempted murder, but it has now turned into a murder investigation despite the efforts of medics to save the victim.
'The woman’s family are being supported by police officers while enquiries continue.'
The suspect - a 'local man' who has not yet been identified - remains in custody.
Jessica Wragg. a shaken customer present at the time of the incident, described how she had to 'dart' out of the Aldi supermarket following the alleged stabbing.
'World has gone mental just had to dart out of Aldi in Skipton some one has been stabbed right next to me on one of the aisles,' she claimed.
An Aldi spokesman earlier told Mirror Online, 'We are working with the police following an incident at our Skipton store'.