A recent report on the detection of very-high-energy gamma rays from V4641 Sagittarii (V4641 Sgr) up to ≈0.8 PeV has made it the second confirmed "PeVatron" microquasar. Here we report on the observation of V4641 Sgr with X-Ray Imaging and Spectroscopy Mission (XRISM) in 2024 September. Thanks to the large field of view and low background, the CCD imager Xtend successfully detected for the first time X-ray extended emission around V4641 Sgr with a significance of ≳4.5σ and >10σ based on our imaging and spectral analysis, respectively. The spatial extent is estimated to have a radius of 7' ± 3' (13 ± 5 pc at a distance of 6.2 kpc) assuming a Gaussian-like radial distribution, which suggests that the particle acceleration site is within ~10 pc of the microquasar. If the X-ray morphology traces the diffusion of accelerated electrons, this spatial extent can be explained by either an enhanced magnetic field (∼80 μG) or a suppressed diffusion coefficient (∼1027 cm2 s‑1 at 100 TeV). The integrated X-ray flux, (4–6) × 10‑12 erg s‑1 cm‑2 (2–10 keV), would require a magnetic field strength higher than the Galactic mean (≳8 μG) if the diffuse X-ray emission originates from synchrotron radiation and the gamma-ray emission is predominantly hadronic. If the X-rays are of thermal origin, the measured extension, temperature, and plasma density can be explained by a jet with a luminosity of ∼2 × 1039 erg s‑1, which is comparable to the Eddington luminosity of this system.