There is no minimum other than the smallest unit of NXT 0.00000001 NXT. This represents 0,00000000000072 BTC.

The issue is that the minimum fee of 1 NXT is still required for such a transaction.

Currently the minimum transaction fee is 1 NXT. There are talks about lowering the 1nxt fee, to increase the usage of certain nxt services like messaging. It wouldn't be ideal to cost 5-10cents every time you sent a message.

Right now the fees are as follows:

All NXT transactions cost 1 NXT

Except for when issuing an Asset, which cost: 1000 NXT - which is about $50 USD which greatly prevents asset spam.