The 27-year-old mother was sleeping with the child when their house caught fire.
Eight other houses were also burnt during the 11pm incident.
Area chief Joseph Waithaka, confirming the incident, also said that property of unknown amount was destroyed after residents failed to put it out.
He said that the deceased had tried to get out of the house in vain since the main door had caught fire.
He said it was not clear how the fire started but the two were asleep and Neighbours only heard cries immediately the fire broke out.
He said the fire then spread to the other wooden houses.
The chief noted that the high intensity wind blowing had made the fire spread to the other houses whose occupants had already moved out.
He said that it took over five hours for the residents to put off the fire as there was no source of water nearby.
Area residents have called on the Laikipia County Government to purchase fire fighting equipments to prevent such occurrences.
The bodies were moved to Nyahururu District Hospital mortuary.