Well I can relate and I really hope this is not affecting her grades. When my daughter was in 4th grade she had a similar issue but I went straight to her teacher. The teacher was very proactive. That day she pulled all 4 girls aside, including my daughter, and talked to all of them. She heard all sides of the story, the one girl admitted to spreading rumors, apologized and the teacher made it very clear that under no circumstances will she tolerate that type of behavior. She said next time this happened, she would go straight to the principal. The girl even apologized to may daughter later that day.
Never had any problems after that. My daughter is in 8th grade, and so far, so good!!
I should also mention I enrolled my daughter in martial arts, coached her through different scenarios at home and we talked about it almost daily. My daughter now feels confident that she can handle almost any situation that arises and has said she will never again let another person control how she feels. She’s learned to just walk away.
Be there for your daughter. She is only in elementary school! Let her know you are on her side, coach her and guide her. You will be doing her a great favor and teaching her how to handle these situations on her own in Middle School.