The total alcohol extract obtained from the aerial parts of R. stricta and fractions of the liquid–liquid fractionation process were tested against picornavirus-causing foot-and-mouth disease (FMD) based on the traditional use of the plant in Saudi Arabia. The most active petroleum ether soluble fraction was subjected to chromatographic purification, and nine compounds were isolated, identified using various chemical and spectroscopic methods, and tested for their anti-viral potential. The new ester identified as α-Amyrin 3-(3′R-hydroxy)-hexadecanoate (1) was the most active compound with 51% inhibition of the viral growth and was given the name Rhazyin A. Compounds with ursane skeleton were more active than those with lupane skeleton except in the case of the acid derivatives where betulenic acid showed 26.1% inhibition against the viral growth, while ursolic acid showed only 16.6% inhibition. Moreover, molecular docking analysis using a glide extra-precision module was utilized for investigating the possible molecular interactions accounting for anti-viral activity against picornavirus of the nine isolated compounds. Molecular docking studies revealed a strong binding of the discovered hits within the active site of FMDV 3Cpro. Compound 1 showed the lowest docking score within the nine isolated compounds comparable to the two known anti-viral drugs; glycyrrhizic acid and ribavirin. The results of this research will provide lead candidates from natural origin with potential safety and efficacy compared to the synthetic ones with lower production costs for managing FMVD.