We do not know for certain, but there are strong arguments that say that this is not so. It has been known for decades that if you combine the constant of Gravity, the speed of light and Planck's constant in the right way with the right powers, you can create a 'Planck Length' which has a size of 1.6 x 10**-33 centimeters. This is 20 powers of ten smaller than an atomic nucleus. Physicists believe that at this scale, the quantum indeterminacy we have come to accept in the atomic world, and in the description of matter and energy, finally carries over into how we must now describe space and time. Space no longer has a nice, smooth geometry, but becomes an uncertain froth of geometric and gravitational distortion with quantum black holes and worm holes shredding up space-time making it into something resembling swiss cheese. We don't know for certain exactly how to describe nature at this scale because we do not have a theory that describes all of the fundamental forces and gravity in a consistent way, although 'string theory' has currently been offered as the prototype for such a theory.
If the Planck Scale is fundamental, then there are no physical objects, fields, particles, space or time that can be infinitely subdivided below the scale set by the Planck length. We have reached the lowest rung on the latter, and all that we may ever know about the universe is bounded between 10**-33 centimeters, and the scale of the horizon to our observable universe at 10**28 centimeters.