The 30-year-old was attacked in the store in Skipton, North Yorkshire, at about 15:30 GMT on Thursday.
"The suspect was initially detained by courageous members of staff and public before he was arrested by officers who were quickly on scene", they said.
A spokesperson said: "We are working with the police following an incident at our Skipton store".
Willsher, who worked at the supermarket, was attacked at the store in Keighley Road just after 3:30pm on 21 December.
Cops arrived within minutes, and the suspect was initially arrested on attempted murder charges, authorities said.
Willsher was married and had a young daughter.
Officers are continuing to investigate the stabbing but said they are not treating it as terrorism or a hate crime.
Woman dies after being stabbed to death in Aldi supermarket in Yorkshire
Skipton Mayor Andy Rankine said the whole town was in shock over the death.
After his wife's death, Mr Willsher changed the picture on his Facebook page to show them sitting closely side by side, smiling into the camera.
Another customer said she had seen Mrs Willsher earlier that day wearing a Christmas jumper at work.
A witness who did not want to be named described hearing "loads of screams" and seeing a woman lying on the floor and a man pinned down as "everyone screamed and ran".
Richard Gardner said: "I woke this morning hoping that yesterday was all just a bad dream Jodie Willsher". I was so scared I ran off.
"Christmas this year will an ordeal for many residents". "All the staff were racing about not knowing what to do", she said.
Floral tributes to Mrs Willsher have been left at the edge of the police cordon around the store, which is closed until further notice while police continue their investigation. It's unclear if she knew her attacker. We will all love and miss you forever, but we will all be thankful everyday that we got to have you in our lives!
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