After kids learn to read, they need to learn how to "read to learn" which is a valuable skill that they will need all through school.
Even though she is a good reader and is reading to herself, she may not yet understand how to comprehend what she is reading.
All of the ideas that have been mentioned are good ones.
Read aloud to her or listen as she reads out loud to you. Then, discuss what you've read together so that she can begin to see what she needs to pick up on as she is reading. As you read the stories, in addition to the specific-type questions like "What was the name of the character?" or "Where were they going?", ask questions like "What do you think is going to happen next?" "Why do you think the character did what he did?" "How would you feel if that happened to you?"
Once she starts understanding the types of things she needs to be paying attention to or looking for as she reads, then you can start having her read short, easy-to-read stories silently to herself and then gradually increase the difficulty of the books as you see she is comprehending what she's reading.
Because she's not also hearing the words spoken, comprehension from reading silently is harder than comprehension from out-loud reading. It's a lot easier for your mind to drift when you read silently.
Additionally, there are all kinds of sites out there that have reading comprehension helps. Here is one link that has free, printable reading comprehension worksheets...
http://www.superteacherworksheets.com/2nd-comprehension.html
When I taught kindergarten, we would receive "Weekly Readers". The "Weekly Readers" came with additional practice reading comprehension worksheets which I would do with the students.
Some other fun ideas - When she reads a book, have her draw a picture from one scene of the book, maybe her favorite scene or the most exciting scene, the scariest scene, etc. Let her make a "sequence booklet" for the story.
There are also the "Summer Bridge" workbooks - the workbooks have more than reading though (math, language, etc.) but the reading worksheets are really good.