What is the lowest mass that an object can have and still be a star?

The lowest mass that an object can have to be considered a star is 0.08 solar masses.    

Explanation:

A star is get when it reaches the necessary temperature in its core to nuclear reaction began.

A Nuclear reaction is the fusion of lighter elements into heavier elements.

In stars there is an equilibrium between two forces, the force of gravity in the inward direction due to its own mass and the radiation pressure in the upward direction as a consequence of the nuclear reaction in its core, which is known as hydrostatic equilibrium.

Therefore, the mass of the star must be enough to the force of gravity act in the inward direction, which leads to the increase in pressure, density and of course temperature in the core, allowing the nuclear reaction to begin.

Hence, the lowest mass that an object can have to be consider a star is 0.08 solar masses.