Let's do a 0th order approximation: the size of a tectonic plate depends on the size of the underlying convective cell (image source).
If we look at the distribution of flow velocities across the cell, we see that the velocity is higher at the borders and practically null at the center. This is due to the shear stress between the upward and downward flow.
One can easily imagine that if the cell is too compact, the convection motion will be hampered by the friction, and thus won't happen.
To understand which of the two phenomena prevails, one can refer to the ratio between the Reynolds number
Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, which is known as a boundary layer. $Re = $$ \rho \cdot u \cdot L \over \mu$
and Nusselt number,
Nusselt number (Nu) is the ratio of convective to conductive heat transfer across the boundary layer. $Nu =$$h \cdot L \over K$
$Re\over Nu$$=$$\rho \cdot u \cdot K \over h \cdot \mu$.
- $\rho$ is the density of the fluid
- $u$ is the velocity of the fluid
- $K$ is the thermal conductivity of the fluid
- $\mu$ is the dynamic viscosity of the fluid
- $h$ is the convective heat transfer coefficient of the flow
If the ratio is bigger than 1, it means the viscous forces are not strong enough to stop the flow, while on the other case, when the ratio is lower than 1, it means that the viscous forces stop the flow and heat transfer happens mostly by conduction.
To have convective cells one need to be in the first case, so, once the material is chosen, this practically set a limit on how small the cell can be.
The parameters affecting the phenomena are listed above, and again all depend on the material. Therefore it might be possible that, with the right materials, convective cells can be small enough that they can be counted in the order of thousands.
However, since you specify that
The planet is earth-like in terms of size and mass
I am afraid there are no knobs to turn, and for such a planet the size of the plates is bound to be similar to what we have on Earth, where one of the smallest one is the Juan de Fuca Plate
One of the smallest of Earth's tectonic plates, the Juan de Fuca Plate is a remnant part of the once-vast Farallon Plate, which is now largely subducted underneath the North American Plate. Approximate area 250,000 $km^2$