The Coronavirus Disease 2019 (COVID-19) caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has led to the loss of life and has affected the life quality, economy, and lifestyle. The SARS-CoV-2 main protease (Mpro), which hydrolyzes the polyprotein, is an interesting antiviral target to inhibit the spreading mechanism of COVID-19. Through predictive digestion, the peptidomes of the four major proteins in rice bran, albumin, glutelin, globulin, and prolamin, with three protease enzymes (pepsin, trypsin, and chymotrypsin), the putative hydrolyzed peptidome was established and used as the input dataset. Then, the prediction of the antiviral peptides (AVPs) was performed by online bioinformatics tools, i.e., AVPpred, Meta-iAVP, AMPfun, and ENNAVIA programs. The amino acid composition and cytotoxicity of candidate AVPs were analyzed by COPid and ToxinPred, respectively. The ten top-ranked antiviral peptides were selected and docked to the SARS-CoV-2 main protease using GalaxyPepDock. Only the top docking scored candidate (AVP4) was further analyzed by molecular dynamics simulation for one nanosecond. According to the bioinformatic analysis results, the candidate SARS-CoV-2 main protease inhibitory peptides were 7–33 amino acid residues and formed hydrogen bonds at Thr22–24, Glu154, and Thr178 in domain 2 with short bonding distances. In addition, these top-ten candidate bioactive peptides contain hydrophilic amino acid residues and have a positive net charge. We hope that this study will provide a potential starting point for peptide-based therapeutic agents against COVID-19.