Hello,
If the system you are referring is not a live syatem, then firstly you will have to delete all the transaction data where ever the object is used(you can get the details using the where used button when you are in the infoobject display screen) and then you have to delete the master data. The reason behind is, master data cannot be completely deleted till it's SID's are being used in any other InfoProviders.
If the system is a live production system, you will have to check your transformation and reload the data.
Regards
Balu