Need help fixing an issue

If your document is set up as facing pages, you can set the inside bleed to zero in the export dialog, ordinarily you don't need to worry about inside bleed (as already mentioned). Zoom in on your spine and confirm the elements are not crossing over onto the facing page, snap them to the exact edge of the page (this is a very common error, in my experience).

Alternately, if your document has two-page spread images, you can shuffle the pages so the color from the facing page won't spill over onto the bleed of the page next to it (create a mix of spread and single pages).

If you are indeed sending this to a professional printer, and it's a saddle-stitch booklet, and you are indeed including bleed in your PDF export (as you should, for full bleed professional printing), this sliver – which is picking up from the facing page – won't be an issue as long as it's beyond the trim of the page. Create your PDF with Trim marks selected, and you will see where the sliver actually is. Professional printers use imposition software that arrange your single page PDFs into printer's signatures/flats, and will actually crop off that sliver anyway as it will be at the fold of the booklet. In that case, what you are seeing in your PDF is actually normal behaviour the way ID is designed right now. I personally would prefer if there was an option to suppress items from facing pages that merely touch the edge (like your photo does) but do not cross over, because these slivers have been known to cause more trouble than one would think (I come from a prepress background), but there ya go. When it would REALLY be an issue, is if you are printing a booklet that's like a coil bound booklet where each sheet is printed just front and back... the sliver may NOT get trimmed off properly and could wind up being seen. Again, professional printers have tools to deal with that, but it'd be nice if ID would take care of that. 😉

Can you tell us a little more about the setup of your document. Is it printing a bleed? If so, is it pulling in the graphic from the adjacent page?