Background: The Greek National Health System (NHS) has been profoundly affected by the synergy of the economic and refugee crises. We aimed at evaluating the public interest regarding refugee and healthcare issues in Greece. Methods: Google Trends was employed to normalize traffic data on a scale from 0 to 100, presented as monthly relative search volume (RSV) for the search term queries: “refugees”, “health”, “diseases”, “hospital”, and “economic crisis” in Greece, from the period 2008 to 2020. Cross-country comparisons in selected European countries were made. Results: The analysis of RSV data showed an upward trend for the keyword “refugee”, in Greece, in the last five years, with two remarkable peaks from 2015 to 2016 and from 2019 to the present. Interest regarding refugees was more prevalent in the Aegean islands compared to the mainland. The mass influx of refugees has been linked to disease-related concerns. The search terms “hospital” and “health” have been the most popular and constantly quested topics since the beginning of the economic crisis in Greece, in 2009. Similar trends existed across Europe. Conclusion: There is an urgent need for effective public awareness of current politico-ethical and social-economic conditions. The patterns of public interest can formulate public policy.