Most likely the same level as you need to be to buy all other NX stuff, which doesn't require any level if I recall correctly. If Nx does require a level it usually mentions that in the description.
Other then that they usually never give it a too high level requirement, so you should absolutely be fine after level 16 which shouldn't take longer then a day.
Edit: Actually, I recall seeing a notice about a certain CashShop item that required level 30+ but I'm not sure if it was the Cash bag or the Master Key...
Final Edit: Checked again and it's on their site. Level 30+ can buy Master Keys.
Other then that they usually never give it a too high level requirement, so you should absolutely be fine after level 16 which shouldn't take longer then a day.
Edit: Actually, I recall seeing a notice about a certain CashShop item that required level 30+ but I'm not sure if it was the Cash bag or the Master Key...
Final Edit: Checked again and it's on their site. Level 30+ can buy Master Keys.