It is common to prepare flow duration curves from a set of daily river flow data, but does it make sense to build a flow duration curve from a set of monthly minimum flow data? I searched on internet, but the key word "minimum flow duration curve" does not return any relevant document.
I believe it is not very useful while FDC's are mostly interesting for the entire discharge record. You can zoom in to the lower part of the curve and analyse it. The problem with the FDC is that it give no indication of sequences of low flows. You can imagine a river with no discharge (=0) during a couple of months for example. With monthly minimum values this problem is smaller.
In the end I believe it's more useful to use probability distributions for frequency analysis of extreme values like low flows. In literature you can find that the Gumbel distribution of the smallest value is one of the most reliable for annual minimum flows.