The rapid outbreak of the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in China followed by its spread around the world poses a serious global concern for public health with almost 90000 people infected and thousands of fatalities. To conquer viral infections, the inhibition of proteases essential for proteolytic processing of viral polyproteins is a conventional therapeutic strategy. To this date, no specific drugs or vaccines are available to treat SARS-CoV-2 despite its close relation to the SARS-CoV-1 virus that caused a similar epidemic in 2003. Thus, there remains an urgent need for the development of specific antiviral therapeutics to conquer SARS-CoV-2. In order to find novel inhibitors, we computationally screened a compound library of over 687 million compounds for binding at the recently solved crystal structure of the main protease of SARS-CoV-2. A screening of such a vast chemical space for SARS-CoV-2 protease inhibitors has not been reported before. After shape screening, two docking protocols were applied followed by the determination of pharmacokinetically relevant molecular descriptors to narrow down the initial hits. Next, molecular 1 dynamics simulations were conducted to validate the stability of docked binding modes and comprehensively quantify ligand binding energies. After evaluation of off-target binding, we report a list of 11 drug-like compounds with improved binding free energy to the target protease in contrast to the cocrystallized peptidomimetic lead compound that suffers from poor pharmacokinetic properties. Furthermore, we identified one potent binder with comparable properties from the natural compound library.