The 57-year-old man, from Burnley, was initially arrested on suspicion of attempted murder but has now been detained for 28 days under Section 2 of the act for an assessment of his mental health.
Police say the stabbings are not being treated as a terrorism incident, but confirmed that counter terrorism detectives had been leading the investigation.
Supt Stasia Osiowy has sought to clarify the situation, saying: "This is not being treated as a terrorism incident but due to some comments made at the scene counter terrorism detectives will be leading on the investigation.
"At this time we are keeping an open mind as to motivation but what I can say is that we are considering the mental health background of the man we have arrested."
Today (December 3), following consultation with mental health professionals, the force has detained the man for 28 days under the Mental Health Act. He will now undergo a thorough assessment of his mental health before Lancashire Police decide how to proceed with the case.
What happened at Marks & Spencer?
Officers rushed to the Marks & Spencer in Burnley town centre at 9.30am yesterday (Wednesday, December 2) after two women were stabbed inside the store.
The victims - a staff member in her 40s and a member of the public in her 60s - were taken to hospital with serious stab wounds. One has now been discharged and the other remains in hospital.
The attacker was detained by members of the public and store staff whilst police were alerted. A knife was recovered at the scene by officers.
The store closed yesterday but has re-opened this morning, and Lancashire Police say there will continue to be extra police patrols in the town centre to offer reassurance to businesses and shoppers.
What is the latest from police?
Supt Stasia Osiowy, of East Police, said: "Our enquiries 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.
"If anyone has information or concerns then please do speak to an officer."
Anyone with information should contact police on 101 quoting log 0313 of December 2 or independent charity Crimestoppers on 0800 555 111.
You can also submit information and video footage via the force's Major Incident Public Portal (MIPP) here.