I think the minimum amount of bitcoins you can send in a transaction is 5320 satoshies. At least I was told the reason counterparty is using that amount for their colored coins is exactly that.
It was 5430 satoshis. The reason for this was because Bitcoin used this as a dust limit for the output. If the threshold isn't met, the client would see it as non standard and not relay it at all, thus hindering the chances of it getting confirmations. Given that majority of the network runs Classic 0.12 or Core 0.12, the dust limit is currently 546 by default with 1000 satoshi being the minimum relay fee. The dust limit would increase if the user rises the relay fee.
I think the OP is wanting to create a non-coinbase tx that either has no outputs or perhaps an output with 0 as the amount (for what purpose?).
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AFAIK, it isn't possible to create a transaction with no outputs and have it confirmed but it is possible to create a transaction with 0 satoshi as output but it is considered non standard.