I'm getting this too - It happens after I attempt to open it. Where before I would get a message saying something like, "this software comes from a 3rd party source are you sure you want to open it" (not exact wording but you get the idea) now it says, "calibre.app will damage your computer. You should move it to the Trash." You have the option of hitting 'cancel' or "Move to Trash" and that's it.
For the record, (regarding above comments) yes I downloaded from the official site and no I did not download from any ads.
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