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Emergency services were called to the store on Keighley Road at 3.27pm today (Thursday 21 December 2017).
The suspect, who is aged in his 40s, was initially detained by staff before being arrested by the police. He has been taken into custody for questioning.
The victim, who is believed to be aged in her early 30s, is receiving treatment for serious injuries.
A police scene guard is in place at Aldi while enquiries continue.
Witnesses or anyone with information that could assist the investigation are urged to contact North Yorkshire Police on 101, select option 1, and speak to the Force Control Room.
Alternatively, contact Crimestoppers anonymously on 0800 555111.
Please quote reference number NYP-21122017-0274 when providing details about this incident.