"We favour an hypothesis that is not an accident," prosecutor Michel Valet told reporters on Monday, according to a report in the local La Depeche du Midi newspaper.
The partner of the girl's mother is now in custody on suspicion of murder.
He is suspected of having killed the girl by firing a bullet through a bathroom door where the mother, her daughter and two sons aged 6 and 2 were trying to hide from him.
The suspect has been held in custody since Monday night as police await testimony from the mother, who is currently hospitalised in a state of shock.
According to the newspaper the man is reported to have flown into a rage following an argument related to the cleanliness of the apartment.
The police were called to the apartment in the Empalot area of Toulouse at around 5.15pm on Monday and arrived to find the girl, named as Shaloma C, bleeding profusely from a head wound.
Despite the efforts of the emergency services, the toddler's life could not be saved and she died in the apartment.
The murder is the latest in a spate of child killings which have shocked France, according to the AFP news agency.
A 47-year-old man was found hanged on Tuesday in Tarbes in the Pyrenees after escaping from a clinic following his arrest on suspicion of murdering his five-month-old son.
The man had left a suicide note indicating that he had strangled the baby, whose body was found in a hotel room in the outskirts of Tarbes on Sunday.
A two-year-old toddler died last week in Lespinasse after being driven into a canal by the suicidal girlfriend of the baby's father.