Scribus as of the writing of this article does not have a built-in drop shadow method. Certainly, one can use Gimp or Inkscape to create some drop shadow-like effects, then import as an image. Here I'd like to show a method which you might consider, created entirely within Scribus.
We are going to use gradients to accomplish this. The difficulty is that, if we wanted to create this for a rectangular object, as most content is, there is no suitable gradient that works in this fashion, where we have horizontal fading at the vertical edge and vertical fading at the horizontal edges.
I will warn at the outset that this is hardly a perfect method, but what we will do is to create a square template from triangular elements, and arrange the gradient in each part so that we end up with the edge gradients all going in the correct direction. It's a bit of work, but what you will have at the end is a grouped object you can save in your Scrapbook, then reuse and resize as needed, sort of a make once, use many approach.