A mother has admitted smothering her 15-month-old daughter and throwing her body in a Melbourne creek.

Sofina Nikat, 24, on Friday pleaded guilty to infanticide over the death of Sanaya Sahib in 2016.

Nikat took the infant to a Heidelberg West park on April 9, 2016 and played with her before covering her airways until the child stopped moving, prosecutor Kerri Judd QC told the Victorian Supreme Court.

"She put her hand over her mouth so as to block the airway," Ms Judd said.

Advertisement

"She continued to apply pressure until Sanaya could not breathe anymore.

"She then rolled her body into the creek."

The Fijian-born woman was originally charged with murder but prosecutors earlier in September accepted Nikat had been suffering from a depressive illness at the time Sanaya was killed.

The maximum penalty for infanticide is five years' imprisonment.

After killing Sanaya, Nikat walked back to the home of a relative and said a man had snatched the girl, Judd said.

Nikat told police a barefoot man of African appearance who smelt of alcohol had snatched Sanaya from her pram.

Police initiated a search with help from members of the public.

A family who had joined the search found Sanaya's submerged body in the creek in the early hours of the next day.

Nikat continued to say someone had snatched her baby before admitting what she did a week after the killing.

"She said she had covered Sanaya's mouth and nose, and had thrown her into the creek," Judd said.

"She thought her baby was possessed."

A Muslim cleric in Fiji had previously told Nikat's parents Sanaya was "under an evil eye", prompting them to send her an amulet of holy water to used on the baby.

Counsel for Nikat, Christopher Dane QC, said the young mother struggled after moving to Australia because she was treated like a servant by her in-laws.

Nikat had an arranged marriage with Sanaya's father and the pair separated while she was pregnant.

She and Sanaya had been living in women's refuges in the months before the killing.

"The events further fed into her frustration, isolation, helplessness, confusion and irrationality," Dane said.

"She threatened on numerous occasions that she wanted to kill herself and her baby."

Nikat could avoid a jail term, with the defence asking Justice Lex Lasry to consider a community correction order.

She has already spent 529 days in custody.

The prosecution wants Nikat jailed.

The maximum penalty for infanticide is five years' imprisonment.

Nikat will be sentenced at a date to be fixed and has been granted bail.

WHERE TO GET HELP:

If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call police immediately on 111.

OR IF YOU NEED TO TALK TO SOMEONE ELSE:

LIFELINE: 0800 543 354 (available 24/7)
• SUICIDE CRISIS HELPLINE: 0508 828 865 (0508 TAUTOKO) (available 24/7)
YOUTHLINE: 0800 376 633
• NEED TO TALK? Free call or text 1737 (available 24/7)
KIDSLINE: 0800 543 754 (available 24/7)
WHATSUP: 0800 942 8787 (1pm to 11pm)
• DEPRESSION HELPLINE: 0800 111 757​