Police say a 24-year-old man was detained on suspicion of driving under the influence of drugs following the incident. He has since been released pending further investigations.
The child was taken to Alder Hey Chilrden's Hospital in Liverpool, while the woman was flown by air ambulance to the Royal Preston Hospital.
She is being treated for a serious head injury. An appeal for witnesses has been issued.
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The incident happened at at around 3:35pm yesterday in Lyons Lane South near to Morrisons supermarket.
The road remained closed for several hours after the collision and people were asked to avoid the area.
A police spokesman said: "We were called at around 3:35pm to the report of a collision between a car and a pedestrian with a pram on Brooke Street, Chorley.
"A child who was inside the pram has been taken to Alder Hey Children's Hospital and the pedestrian, a woman, has been taken to Royal Preston Hospital by air ambulance.
"A 24-year-old man has been arrested on suspicion of driving with excess drugs."
Anyone with information is asked to call 101 quoting incident reference 887 of November 6th."