A three-year-old Mthatha girl was killed and her four-year-old sister seriously hurt when their mother allegedly beat them with a broomstick, Eastern Cape police said on Sunday.

The mother was arrested on Saturday, hours after the crime, Superintendent Mzukisi Fatyela said.

"It is alleged that the sisters were eating the food of the younger sister, aged nine months, when the mother got angry. She beat them with a broomstick and one girl died."

The four-year-old was in a serious condition in hospital. The baby was placed in her grandmother's care.

The woman was expected to appear in the Mthatha Magistrate's Court on Monday.