UNAIDS has identified the Danish HIV epidemic in men who have sex with men (MSM) as a priority for elimination. Incidence is close to the elimination threshold of one new infection per year per 1,000 individuals. However, surveillance data show that HIV strains are being imported into Denmark, mainly due to travel. We use a transmission model to predict (from 2018 to 2030) the impact of pre-exposure prophylaxis (PrEP) on incidence. Our model reflects the current epidemic and diagnosis rates in the Danish MSM community. We conduct a sensitivity analysis based on 20,000 simulations, and assume that PrEP coverage could range from zero to 50% and diagnosis rates increase up to three-fold. We predict that incidence will fall below the elimination threshold, even without the introduction of PrEP, reaching 0.87 (median, 95% Confidence Interval: 0.65-1.23) new infections per 1,000 MSM by 2030. PrEP could reduce incidence to well below the threshold, if it results in a significant increase in diagnosis rates and reduces the number of infections occurring abroad. The Danish Medicine Agency and Danish Health Authority have recommended introducing PrEP. Our study provides strong support for this recommendation, and shows the importance of Danish MSM using PrEP when abroad.