The socialist deputy was only appointed less than a fortnight ago in a reshuffle after a revolt over austerity measures threw the French government into crisis.
A government source told AFP that he stepped down after admitting he had a "problem about the declaration of his taxes he has not resigned because of any political disagreement".
The resignation has uncomfortable echoes of the so-called Cahuzac affair, when Hollande's budget minister Jerome Cahuzac was sacked in March 2013 after he was accused of evading tax using non-declared Swiss bank accounts.