More than two dozen workers at the plant in Tamil Nadu state have spoken out about harassment since the 20-year-old's body was found near her home on 5 January, a labour rights group said, as H&M pledged "an independent third-party investigation".
"Any future relationship with this supplier will entirely depend on the result of that investigation," the company said in a statement, adding that it was in touch with the factory and did not tolerate harassment of any kind.
Police said a man who worked at the plant had been arrested on suspicion of murder in the case.
"Our investigations show the two were in a relationship and the motive for the murder was personal difference that arose between the two," a police officer said, asking not to be named because he was not authorised to speak to the media.
He said they had not received any complaints of sexual harassment from employees of the garment factory or their union, but a regional rights groups said numerous workers had reported such incidents.
"The girl's mother and co-workers have said she had confided in them about the harassment," said Nandita Shivakumar, India coordinator of the Asia Floor Wage Alliance that works for garment workers' rights in the region.
"At least 25 other workers we have spoken to told us about the harassment they have faced in the factory and we feel that the brand and manufacturer have failed to create an enabling environment for workers to complain," she added.
India's multi-million-dollar garment industry, which employs at least 12 million people, has often faced scrutiny for labour rights abuses and sexual harassment cases affecting its largely female workforce.
Labour rights campaigners have raised concerns that growing pressure from big brands on suppliers to deliver clothes quickly and cheaply is fueling exploitation - from a lack of bathroom breaks to verbal and sexual abuse.
They also point to poor implementation of a 2013 law to combat sexual harassment at work, which requires employers with at least 10 workers to set up women-led complaint committees with the power to fine or fire those found guilty of harassment.
"There is a fear of retaliation in most cases and in some there is lack of awareness of how to use this law," said Shivakumar.
"There were verbal complaints made to supervisors in this factory that were not taken seriously or forwarded to the internal complaints committee."