Yes, A bigger rear tire can be put on the Ninja 250. The stock rim will accept up to a 150mm tire. A 140mm tire will fit just fine with no issues or modifications. A 150mm tire will fit, but it is very close to rubbing the swing arm. You can read about a 150mm rear tire here (Thanks to Ajai): http://www.newninja.com/modifications/150-rear-tire
A good idea to get the most out of a 150mm tire is to also install a wider rim. This causes the profile of the rear tire to be 'flatter', actually increasing grip. You can find information on installing a wider rim here (Thanks to eric): http://www.newninja.com/modifications/wider-rear-rim-and-tire
A good idea to get the most out of a 150mm tire is to also install a wider rim. This causes the profile of the rear tire to be 'flatter', actually increasing grip. You can find information on installing a wider rim here (Thanks to eric): http://www.newninja.com/modifications/wider-rear-rim-and-tire