The 57-year-old was arrested on suspicion of attempted murder after a member of staff in her 40s and a shopper in her 60s suffered stab injuries at the store in Burnley on Wednesday morning.
On Thursday, a spokesman for Lancashire police said the man had been detained for 28 days for an assessment of his mental health.
The incident is not being treated as terror-related and inquiries are continuing.
One of the victims remains in hospital and the other has been discharged, the force said.
The man was detained by members of the public and staff and a knife was recovered at the scene.
Superintendent Stasia Osiowy said: “Our inquiries into this incident are ongoing and I would like to continue to appeal to members of the public who may have seen or filmed this incident, or who have information which could assist, to get in touch with us.
“Mercifully, while the injuries caused in this incident were serious, they are not life-threatening and the two women involved are continuing to receive the support of specially trained police officers.
“I would like to stress again this is not being treated as a terrorism incident and we continue to keep an open mind as to motivation of this individual.
“I would like to thank the community for their understanding and co-operation while we dealt with an incident which clearly had the potential to cause a great deal of concern.
“We will continue to update people on the course of our investigation as and when we can and there will continue to be extra patrols in the town centre to reassure.”
Anyone with information or video footage is asked to contact police on 101 quoting reference 0313 of December 2.