Google have announced that as of November 1st any site with a pop-up prompt asking users to download their mobile app will have their search rankings affected.
After November 1, mobile web pages that show an app install interstitial that hides a significant amount of content on the transition from the search result page will no longer be considered mobile-friendly.
They go on to to say that their mobile friendly algorithm and testing tool will take this into consideration for sites now too. Google also advised that smaller and less intrusive banners at the top of a mobile page should be used instead of pop-ups and interstitials and these would not be penalized.
Examples of bad and good app download prompts from Google.