The knife attack occurred on an SJ train en route from Stockholm to Copenhagen. The police were alerted to the suspected assault shortly before 6pm.
"The man produced a knife as he was being ejected from the train at Lund station due to his unruly behaviour. Aside from the injured woman, a further member of the crew was treated for shock. Both have been taken to hospital for treatment, according to Ronny Hörstrand at SJ's press office.
The stabbed woman is being cared for at Skåne University Hospital in Lund.
"A woman in her thirties was admitted to the emergency room in Lund. Her situation is stable," said Anna Möller at Region Skåne's press office.
The 29-year-old suspect is now set to be interrogated by the police. He was initially suspected of assault, but the case has since been reclassified as attempted murder.
The train was held at the station by police following the incident.
"We need to know who had seen what, what they had seen and to collect their testimony," said Linda Pleym at Skåne police.
Police confirmed that further interviews would be conducted on Sunday.