The accused, Anita Waghle, also a resident of Nallasopara, Palghar district, was arrested last night, police said.
The five-year-old girl was kidnapped from outside her home on March 24 and she was found dead in the ladies' toilet of Navsari railway station in Gujarat, over 250km from Mumbai, on Sunday, Additional SP Raj Tilak Roshan told reporters.
The Navsari police initially registered a case of accidental death and sent the body for a post-mortem which revealed the death was due to strangulation.
Later, a murder case was filed, police said.
A probe revealed Ms Waghle had taken the girl to Navsari in a train and strangled her to death in the toilet, police said.
A team of cops led by senior inspector Kishore Khairnar zeroed in on the woman on Tuesday night and placed her under arrest, they said and claimed she has confessed to the crime.
The woman was reportedly in a relationship with the victim's father, an autorickshaw driver, and wanted to marry him. However, he kept delaying marriage and this enraged her, they said. The accused then kidnapped and killed his daughter, police added.