The body of Aisha Alam, 49, was discovered after a man - understood to be her husband - walked into a police station yesterday to report her killing.
The 52-year-old man is being questioned on suspicion of her murder by Manchester police.
Friends said Mrs Alam, who had three daughters and a son, was a teaching assistant at a school for children with special education needs.
She moved to England from Pakistan and had been living in her home in the Manchester district of Levenshulme for 25 years.
Officers discovered her body just after noon yesterday after a man, understood to be her husband, walked into Longsight police station to report she had been killed.
A post mortem which took place last night said Mrs Alam died of multiple stab wounds. Police have named her formally.
Mrs Alam's family were too upset to speak last night, but neighbours spoke of their shock.
'She was quite quiet and kept herself to herself but was such a lovely lady.
'I would always stop and say hello and chat and I would do the same with her daughters as well who are lovely. We are all very shocked and scared by what's happened. I saw her daughter at about 8am and everything seemed fine.
'I went shopping in Longsight and I got back and there were police here asking if I had heard anything next door.
Mrs Alam raised her family in the terraced house and two of her children were believed to still be living at home.
Gerry Hill, 50, who lives opposite, said: 'I've been here five years and there has never been anything remotely like this before.
Crime Scene Investigation teams spent most of yesterday combing the house for clues while officers carried out door-to-door enquiries.
DCI Colin Larkin said: 'A woman has been killed and our thoughts are with her family and friends at what is obviously a totally devastating time for them.