The critical point here is not the mass. It is the mass density and the resulting gravitational force on the atoms your planet is made of.
See this post about the requirements for a black hole
The same basic idea holds for turning a planet into a star.
In detail: If you make up your planet, the more matter (and thus mass) you add, the stronger the overall gravity of your planet becomes.
The stronger the gravity becomes, the more your matter is compressed, increasing the mass density of your planet (and also pressure and temperature, eventually turning solids to liquid to gas to plasma...) increasing the kinetic force of your atoms.
If the gravitational and kinetic force of the protons exceeds the electrostatic forces which keeps your atoms pushed apart, you start a nuclear fusion reaction and your planet becomes a star. Wikipedia has all the details
Conclusion: As long as you do not exceed a gravitational density threshold your planet can be any size you like. The exact numbers will require a non-trivial amount of calculation for any given case.
However, if you are writing fiction and not a documentary, consider an artificial planet-like structure that is mostly hollow for extremely large sizes. This way you will prevent to much matter from concentrating on one point. The limit there is your stellar neighbourhood, with nearby stars starting to mess with the integrity of your construct through gravity.
The largest known planet so far seems to be about 1.7 times the size of Jupiter (Source), which is utterly large.
Of course if you need a solid or liquid surface, or human beings being able to live on it without aid, your planed has to be much smaller.