It is generally believed that any quantum theory of gravity should have a generic feature—a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such that the spacetime acquires a zero-point-length (Formula presented.) of the order of the Planck length (Formula presented.). This prescription leads to several remarkable consequences. In particular, the Euclidean volume (Formula presented.) in a D-dimensional spacetime of a region of size (Formula presented.) scales as (Formula presented.) when (Formula presented.) , while it reduces to the standard result (Formula presented.) at large scales ((Formula presented.)). The appropriately defined effective dimension, (Formula presented.) , decreases continuously from (Formula presented.) (at (Formula presented.)) to (Formula presented.) (at (Formula presented.)). This suggests that the physical spacetime becomes essentially 2-dimensional near Planck scale. © 2016, Springer Science+Business Media New York.