D.H.
My first question is, has someone she was very attached to died recently? Or has she seen on the news about a Mother being killed? Has this started fairly recent or going on for a long time? Ask her why she feels this way. There has to be a reason.......
You need to talk to her........tell her how wonderful it is to be so close, but, that you each have your own things that you need to do.......you as Mommy have many things to take care of and she has so much learning and growing to do....and sometimes that requires you to be apart, or on separate floors of the house or even different parts of the school.
She's young, so I don't know how much telling her that if something is going to happen, neither of you can stop it if it's meant to be......you would know if she would understand that or be able to put it in her language. Like when she falls and scraps her knee when you are there, you couldn't stop it, but you were still there.......understand?
If this doesn't work, you might want to get someone professional to talk to her to make sure it's just a normal concern and not something else.....it is probably just a stage, but if it goes on for months, then I would be concerned.......
She might feel you don't spend enough time with her......maybe you should have a girls night out or something........then see if that helps it at all......
Good Luck and hang in there.