There's no upper limit to the size of object the ship can move, but this is subject to the normal restriction that apply when applying force to large objects; the bigger they are, the harder it is to get them to move.
The TNG Technical Manual presents us with a wealth of information about the deflector system. In essence it consists of two main systems; a series of nested static fields that deflect interstellar dust and hydrogen and a secondary deflector/tractor-beam capable of moving larger objects out of the ship's path.
Although the density of the interstellar medium is extremely low,
significant hazards to navigation exist, especially for a starship
traveling at relativistic or warp velocities. Among these are
micrometeoroid particulates, as well as the much rarer (but more
hazardous) larger objects such as asteroids. Even the extremely
tenuous stray hydrogen atoms of the interstellar medium itself can be
a dangerous source of friction at sufficient velocities.
The navigational deflector, also controlled by the subspace field coils, is a powerful tractor/deflector that sweeps thousands of kilometers ahead of the ship, pushing aside larger objects that may present a collision hazard.
Although the active scanners are generally used to move the ship out of the path of very large objects, the deflectors are approximately twenty-four times as powerful as the ship's primary tractor beam, albeit subject to the same inverse square law degradation of their effect at distance.
The heart of the navigational deflector system is three redundant high
power graviton polarity source generators located on Deck 34. Each of
these generators consists of a cluster of six 128 MW graviton polarity
sources feeding a pair of 550 millicochrane subspace field distortion
amplifiers. The flux energy output of these generators is directed and
focused by a series of powerful subspace field coils.
The main tractor beam emitters are built around two variable phase 16
MW graviton polarity sources, each feeding two 450 millicochrane
subspace field amplifiers. Phase accuracy is within 2.7 arc-seconds
per millisecond, necessary for precise interference pattern control.
Assuming these calculations apply equally, the ship can deflect moderate-sized objects (in the range of tens of kilogrammes) sufficiently to make it worthwhile before the ship gets there. Anything larger wouldn't have moved far enough out of the way to bother and would be avoided through course-correction but there's nothing that stops the Enterprise from trying to deflect a planet, it just wouldn't move very far. Note also that unless you can entirely envelope the object, you also risk it being torn apart