Clarkson, 32, who welcomed a baby girl with husband Brandon Blackstock, 38, on June 12, called her the greatest thing on Earth.
"Here is our beautiful baby girl River Rose, the greatest thing on the planet," she captioned the picture.
River Rose is seen sleeping soundly in a red carriage embossed with a small rose in the photograph. She is dressed in a white dress and wearing a white headband with a yellow flower.