The woman, identified by her mother as 33-year-old Thabita Haruna, was killed on Sunday in Bauchi after she allegedly refused to undergo a security screening at a city market.
Boko Haram has increasingly used women and young girls as suicide bombers against so-called “soft targets” such as crowded bus stations and markets.
But Bauchi State police spokesman Haruna Mohammed said Sunday’s victim was not a bomber.
“All our investigations have proved that this woman was mentally sick and had nothing to do with suicide bombing,” he told AFP, without specifying her condition.
“We as law enforcement agents will not stand by and allow people to take the law into their hands.
“We are continuing with (the) investigation and as soon as the perpetrators of this act are arrested we will take legal action (against) them.”
The woman’s mother, Rahab Haruna, said she hoped the authorities would take “appropriate action”.
“There is law, therefore her assailants should not have taken the law into their hands. They just killed and burnt my daughter,” she added.
She described Thabita as “a normal young woman” who worked as a trader until she became mentally ill, which saw her treated at a psychiatric hospital on and off between 2007 and 2013.
“She would get an occasional bout of the illness and when that happened she would go wild and destroy things. She would gather household articles and burn them.
“When she got out of the fit she would calm down and became normal and help with domestic chores.
“She left home on Saturday, we didn’t know where she went. We looked for her all over our neighbourhood but we didn’t find her until the next day.
“She ended up in Muda Lawal (market) where she was assaulted, humiliated and burnt to death. Before she was killed they searched her and found on her the identification card of her sister Alheri.”
She was traced back to the family home from the ID card, she added.