I don't think I would tell a seven year old I was sick and had to go spend time with a doctor. I think that would have freaked me out as a seven year old.
But the honest truth is that rehab is like school. It teaches you how to cope with life. Is there some version of that which would be acceptable? Like, "I need to take some classes to help us and the classes I need to take for learning how to be a better person/Mommy require me to go and study for XXX days. When I come back, we will go to the [whatever she likes] zoo, amusement park, beach. Which one would you like best?" Sort of a light-handed comment followed by switching subjects to something fun for her.
Alternatively, maybe call the rehab and ask for some sample scripts.