The Nimroz government claimed the books, copies of 11 titles, undermined national integrity and could fuel ethnic problems.
Officials said they were acting on instructions from the ministries of culture and justice.
But ministerial spokesmen have denied this in interviews with the BBC.
Afghanistan authorities claim The books, which circulate freely elsewhere in Afghanistan, were seized six months ago as they were being imported from Iran.
A BBC correspondent says the destruction of the books in this way is thought to be unprecedented.
Nimroz province, which borders Iran, is one of the few Afghan provinces which does not have a permanent presence of international troops.
It has seen an increase in violence over the past few months and is an area where the Taleban have a strong influence.
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