The interaction of p53 and MDM2 is modulated by the phosphorylation of p53. This mechanism is key to activating p53, yet its molecular determinants are not fully understood. To study the spatiotemporal characteristics of this molecular process we carried out Brownian dynamics simulations of the interactions of the MDM2 protein with a p53 peptide in its wild type state and when phosphorylated at Thr18 (pThr18) and Ser20 (pSer20). We found that p53 phosphorylation results in concerted changes in the topology of the interaction landscape in the diffusively bound encounter complex domain. These changes hinder phosphorylated p53 peptides from binding to MDM2 well before reaching the binding site. The underlying mechanism appears to involve shift of the peptide away from the vicinity of the MDM2 protein, peptide reorientation, and reduction in peptide residence time relative to wild-type p53 peptide. pThr18 and pSr20 p53 peptides experience reduction in residence times by factors of 13.6 and 37.5 respectively relative to the wild-type p53 peptide, indicating a greater role for Ser20 phosphorylation in abrogating p53 MDM2 interactions. These detailed insights into the effect of phosphorylation on molecular interactions are not available from conventional experimental and theoretical approaches and open up new avenues that incorporate molecular interaction dynamics, for stabilizing p53 against MDM2, which is a major focus of anticancer drug lead development.