You have some good answers here. I had a son who was tense - it was his personality. What I had to do was understand that he was hard-wired this way. That didn't make it easier for me, but at least I wasn't clueless about it...
I want to recommend to you that you don't allow this to pull her away from responsibility. You won't be doing her any favors if you do. You don't need to talk her to death over it. Just gentle reminders that she will be fine, that she doesn't have to worry - you are there for her. If you try to focus too much on this, she will truly believe something is wrong with her.
This summer, give her a week off from studies (and tell her this up front) and then every day, she needs to do some sommer bridge activities. She needs to be keeping up with her acquired skills and learning some new ones so that the beginning of the next school year isn't so daunting. If you let her go all summer without working on schoolwork, her anxiety could be crushing come August. Instead, she should feel empowered by her knowledge from the summer. For example - has she learned her multiplication tables yet? What about the states and their capitals? (I'm not sure what grade she's in.) What about writing in cursive? Find out what she will be responsible for in the next grade level (ask a mom in that grade - she'll be happy to tell you) and that's where you start. There are CD's you can get that do music and multiplication tables - we did that in the car together everytime we were driving somewhere. You can be taking walks together and recite the multiplication tables. There was a funny book that I bought that taught the states and their capitals - I don't remember the name of it, but it made up silly sentences to help you learn and remember (pnemonic devices.) Both of my kids learned both of these skills over a summer, so they didn't have to stress on either one of these during the school year. Instead, they could work on conceptual stuff like word problems. If she will be learning cursive, Handwriting Without Tears is a terrific way to learn. You can google them and order the books online. Both my kids did that program and really appreciated it. Learning to write correctly takes a lot of stress off of little hands and is a good skill that a lot of schools don't have time to teach anymore.
I made all of this fun, without pressure. However, I made sure the kids understood that this was part of the summer schedule and I expected it of them. We did it first thing in the morning after breakfast, and then after that we went on to other things. I also included plenty of library time so that they could find lots of different books to read.
Schooling should be done all year, with reading the very minimum. That way she won't feel that she is behind in her studies and make her anxiety worse. Just make sure that YOU aren't feuling anxiety by unconsiously making her feel that she has to "grow up". Working on school work and learning new things isn't about "growing up". It's about being a kid...