Charlotte Bevan, 30, left Bristol Maternity Hospital at 9pm last night with her four-day-old child.
Avon and Somerset Police said they were concerned for Ms Bevan's welfare as she and her baby were not dressed for the cold night.
"We have officers searching the area near to the hospital," a force spokesman said.
"Charlotte may appear confused and worried and her baby is inappropriately wrapped for the cold weather. The mother is not wearing any shoes and we have serious concern for the welfare of her baby."
Ms Bevan is described as white, around 5ft 8in tall, of average build with dark wavy hair. She is thought to be wearing a black top and black trousers but was not wearing a coat.
Yesterday morning, the new mum posted a video on her Facebook page called Get Through Positive and Negative Thinking Rough Patches.
She also listened to music videos on YouTube throughout the afternoon.
Heartbroken Pascal Malbrouck has made a desperate appeal for information about his missing wife and daughter.
He said tearfully: "I left the hospital at 8.30pm and they say she left between 8.45 and 8.55pm.
"Nobody saw anything, nobody say nothing. They said she went out of this door and I counted seven cameras but nothing.
"They weren't working. She couldn't have walked far, she went out in flip flops with a baby in her arms.
"If somebody had seen something they should have reported it by now, I just don't know."
Writing on Twitter, Avon and Somerset Police said: "We're appealing to friends of Charlotte who may have been contacted by her to let us know she and baby are okay.
"Call us on 101."