The baby, whose name had not been released, weighed 7 pounds, 12 ounces when she was born at Gloucestershire Royal Hospital.
"The queen, the duke of Edinburgh, the princess royal, [Capt.] Mark Phillips and Mike's parents, Mr. Phillip and Mrs. Linda Tindall, have been informed and are delighted with the news. The baby's name will be confirmed in due course," the palace said in a statement.
Zara is one of the godparents of Prince George, the first son of Prince William and his wife, Kate.