Depends on whose definition you go by. If you define a star as a large gaseous celestial body which undergoes fusion at some point in its life, then the minimum mass is around 13 times Jupiter's mass; below that mass and it will not fuse deuterium early in its life (brown dwarf stars do actually undergo fusion, but their deuterium supply is consumed relatively quickly on a cosmic scale).
http://www.universetoday.com/19237/dense-exoplanet-creates-classification-calamity/
Some try to define it by the method by it formed, but I find that to be a bit silly; not only can that be difficult to definitively determine, but to me the way in which it formed is less important than what it became. If I could be so bold, it would be like saying in biological science that a human cloned and gestated by artificial means in some futuristic "vat" is not actually a human because it didn't form the way humans naturally do.
Oooh, y’know, I just read that in one of the articles related to this... the indistinct answer to that is, deuterium ignition requires more mass than that.