We present results of four-pointing Suzaku X-ray observations (total ~200 ks) of the intracluster medium (ICM) in the Abell 1835 galaxy cluster (kT ~ 8 keV, z = 0.253) out to the virial radius (r_vir ~ 2.9 Mpc) and beyond. Faint X-ray emission from the ICM out to r_vir is detected. The temperature gradually decreases with radius from ~8 keV in the inner region to ~2 keV at r_vir. The entropy profile is shown to flatten beyond r_500, in disagreement with the r_1.1 dependence predicted from the accretion shock heating model. The thermal pressure profile in the range 0.3r_500 < r < r_vir agrees well with that obtained from the stacked Sunyaev-Zeldovich effect observations with the Planck satellite. The hydrostatic mass profile in the cluster outskirts (r_500 < r < r_vir) falls well short of the weak lensing one derived from Subaru/Suprime-Cam observations, showing an unphysical decrease with radius. The gas mass fraction at r_vir defined with the lensing total mass agrees with the cosmic baryon fraction from the WMAP 7-year data. All these results indicate, rather than the gas-clumping effect, that the bulk of the ICM in the cluster outskirts is far from hydrostatic equilibrium and infalling matter retained some of its kinetic energy. Finally, combining with our recent Suzaku and lensing analysis of Abell 1689, a cluster of similar mass, temperature, and redshift, we show that the cluster temperature distribution in the outskirts is significantly correlated with the galaxy density field in the surrounding large-scale environment at (1-2)r_vir.