Try resetting your Illustrator preferences.
To do so:
For Macintosh Users: With Illustrator closed launch a Finder Window in column view and click on your home folder. With the Option Key pressed choose Library from the Finder Go Menu. Within the Library folder find the folder called Preferences and within it find the following two files and delete them: “Adobe Illustrator <Version #> Settings” (earlier versions of Illustrator might just say “Adobe Illustrator”) and “com.adobe.Illustrator.plist”. When Illustrator is next launched it will create new preference files and the program will be restored to its defaults.
After you’ve reset up the program (make sure that no document window is open) to your liking, it is a really good idea to create copies of your personalized “mint” preference files (make sure that you quit the program before copying them—that finalizes your customization) and use them in the future to replace any corrupt versions you may need to delete.
For Windows Users: Hold down Ctrl + Alt + Shift when launching Illustrator and respond affirmatively when asked if you want to reset.
Are you using "RightZoom" - this could be the reason.
I really want to thank you for this comment. I had this for half a year and it was really, really annoying. I was looking for a solution, but couldn't find a solution.
I have the exact same problem in Indesign (only the object moves up and to the left).
RightZoom was the reason. Thank you so much ...
My God This just happens to me. The object moves when I click and I am not using RightZoom...So annoying! Help
Try Ctrl E to toggle out of GPU preview into CPU preview.