Antje Jackelen, who is to be installed as head of the Lutheran Church in Sweden next year, called the attacks "spiteful," TheLocal.se reported Saturday.
"I was not prepared for this spite and hatred. It's clear that I am being personally referred to, it is hard to protect yourself when there is so much aggression,"Jackelen said in an interview with Sveriges Radio P4 Kristianstad.
Jackelen, currently the bishop of Lund, became the first woman to be elected archbishop in October. She is known for views that have angered some of the clergy, including suggesting the virgin birth is a metaphor.
One online attacker said Jackelen should be burned at the stake, the medieval punishment for witches and heretics.
Another did not like her hairstyle.
"Choose Muhammed instead so we can be spared from your ugly old man's haircut," a message on an online board said, referring to the Prophet Muhammad, the founder of Islam.