There is evidence that replacing saturated fat (SFA) with polyunsaturated fat (PUFA) lowers ischemic heart disease (IHD). In order to improve the population's diet, the World Health Organization has called for the taxation of foods that are high in SFA. We aimed to assess the potential health gains of a European fat tax by applying the SFA intake reduction that has been observed under the Danish fat tax to six other European countries. For each country, we created a fat tax scenario with a decreased SFA intake and a corresponding increase in PUFA. We compared this fat tax scenario to a reference scenario with no change in SFA intake, and to a guideline scenario with a population-wide SFA intake in line with dietary recommendations. We used DYNAMO-HIA to dynamically project the policy-attributable IHD cases of these three scenarios 10 years into the future. A fat tax would reduce prevalent IHD cases by a minimum of 500 and 300 among males and females in Denmark, respectively, up to a maximum of 5,600 and 4,000 among males and females in the UK. Thereby, the prevented IHD cases under a fat tax scenario would correspond to between 11.0% (in females in the Netherlands) and 29.5% (in females in Italy) of the prevented IHD cases under a guideline scenario, which represents the maximum preventable disease burden. Henceforth, our quantification of beneficial health impacts makes the case for the policy debate on fat taxes.