If your car is brand new, then it probably is a good time to do an oil change anyways (break in period). If not, you would need to find out what needs servicing. You can go through the menus and there should be something on there to reset the service light or indicate what particular item needs servicing. Could be something as simple as the cabin air filter. Of course, if your car is coughing and sputtering, then you need to have it looked at.
If it comes on only when you start your car from cold, it could be you are low on coolant in the reservoir. But I thought there would be a coolant system icon on the display if that were the case.
Please post a picture of your car so we can tell which generation of MINI we're talking about and admire your ride. ... nevermind. I just looked it up in your profile. Nice car.
If your car is under warranty, get the dealer to fix it.