Cyclin-Dependent Kinase 6 (CDK6) plays an important role in cancer progression, and thus, it is considered as an attractive drug target in anticancer therapeutics. This study presents an evaluation of dietary phytochemicals, capsaicin, tocopherol, rosmarinic acid, ursolic acid, ellagic acid (EA), limonene, caffeic acid, and ferulic acid for their potential to inhibit the activity of CDK6. Molecular docking and fluorescence binding studies revealed appreciable binding affinities of these compounds to the CDK6. Among them, EA shows the highest binding affinity for CDK6, and thus a molecular dynamics simulation study of 200 ns was performed to get deeper insights into the binding mechanism and stability of the CDK6-EA complex. Fluorescence binding studies revealed that EA binds to the CDK6 with a binding constant of K = 107 M−1 and subsequently inhibits its enzyme activity with an IC50 value of 3.053 µM. Analysis of thermodynamic parameters of CDK6-EA complex formation suggested a hydrophobic interaction driven process. The treatment of EA decreases the colonization of cancer cells and induces apoptosis. Moreover, the expression of CDK6 has been downregulated in EA-treated human breast cancer cell lines. In conclusion, this study establishes EA as a potent CDK6 inhibitor that can be further evaluated in CDK6 directed anticancer therapies.