A 20-day-old infant with a high fever was abducted from Harlem Hospital early yesterday, apparently by a woman dressed in white nurse's clothes who had been seen in the hospital for several weeks or months, the police said. A woman was being sought for questioning last night by the police. The child, Carlina White, of 3150 Broadway in Manhattan, was discovered missing from a 17th-floor pediatrics ward sometime after 3 A.M., the authorities said. About two hours earlier, she had been admitted by her 16-year-old mother, Joy, with a 103-degree fever.

Hospital officials said the infant, who had been given an intravenous antibiotic solution through her foot, was abducted before doctors could diagnose her condition. They said it was possible that she had a life-threatening illness. Consoled Baby's Mother

Detectives said they believed the infant had been taken by aheavyset woman. They said hospital staff members told them the woman had been seen repeatedly in the building, wearing a white dress and stockings and a blue-green surgical smock.

''Based on the descriptions, I would say she was basically loitering,'' said Assistant Chief Aaron H. Rosenthal, commander of Manhattan detectives. He said one nurse reported that the woman had been around the hospital since at least March.

The hospital's executive director, Charles Windsor, said the woman had been questioned at least twice. He said she had told a patient's family on one occasion that she was a nurse on the fourth floor, and had told a nurse that she was visiting a family on the 17th floor.

Shortly before the baby was taken, Mr. Windsor said, the suspect consoled Ms. White and gave her tissues to wipe her eyes. He said the mother, who had gone home by the time the infant was reported missing, told officials she had never seen the woman before.

Hours earlier, the police said, the suspect had chatted with the father of a patient in room adjoining that of the abducted infant. At one point, Mr. Windsor said, a nurse came into that room and asked the man what he was doing there. Security Precautions

''He proved he was the father, and then pointed to this other woman and said she was a nurse on the fourth floor,'' Mr. Windsor said. ''The nurse saw her uniform and didn't question her.''

Mr. Windsor said all of the hospital's 4,000 staff workers and doctors are supposed to wear indentification cards and are required to produce them if challenged. Visitors are required to obtain passes. If staff members are suspicious of any person, they are to call the security office.

Mr. Windsor said the hospital could find no record of a formal complaint against anyone matching the suspect's description. The police described her as black, between 25 and 30 years old, about 5 feet 8 inches tall and 180 to 190 pounds. They said she had a light complexion and some hair under her chin.

The infant was described as black, 21 inches long, about 8 pounds, with curly black hair and wearing a sleeveless T-shirt.

Chief Rosenthal said a security guard saw a woman fitting that description walk out of the hospital sometime after 3:30 A.M. He said no infant was seen, but that the woman could have concealed the child in her smock.