The strike by health workers that entered its third week, has paralysed services across the country as the workers push for better working conditions.
Doctors joined nurses and clinical officers in the strike this week, as both the national and county governments threatened to sack them saying the strike was illegal.
The deaths of the babies was reported at the Margaret Kenyatta Mother Baby Wing of the hospital, where services have been scaled down due to the strike.
The hospital receives referral patients from Bomet, Narok, Baringo, Kericho, Nyandarua, Laikipia and Samburu counties.
The deaths were reported a week after patients with birth complications complained of being delayed to be taken to the theater due to shortage of staff.