The 35-year-old woman from Uttar Pradesh did not realise she had been bitten when she woke and breastfed her daughter.
The three-year-old girl and the mother fell ill on Thursday and both died before they could reach hospital, police inspector Vijay Singh said.
The family spotted the snake in another room but the creature escaped.
India is home to some 300 snake species and 60 are highly venomous, including the cobra, krait, Russell's viper and saw-scaled viper. Out of one lakh snakebite deaths around the world each year, India accounts for 46,000, according to a 2011 study by the American Society of Tropical Medicine and Hygiene.