The First Minister raised concerns over the impact on Scottish farmers after a letter emerged from UK Government department Defra which sets out the ban.
It will mean an EU export ban on seed potatoes, which are not intended for consumption, but to be planted in order to grow more potatoes.
"This is a disastrous Brexit outcome for Scottish farmers," Ms Sturgeon said on Twitter today.
"And like all other aspects of Brexit, foisted on Scotland against our will."
The EU will allow almost all other food and plant exports from Great Britain to continue after Brexit transition ends next year.
The seed potato industry is largely focused on Scotland and the north of England.
The Defra letter says: "Unfortunately the EU have confirmed they will not accept our case for a permanent change to the prohibition on seed potatoes… on the grounds that there is no agreement for GB to be dynamically aligned with EU rules.”
The ban will apply irrespective of any Brexit trade deal reached in talks between UK and EU negotiators.
Archie Gibson is executive director of Agriko UK, a supplier of certified Scottish, English and Dutch seed and exporter of seed potatoes in the UK through parent company Agrico Holland.
He said: "It appears seed is prohibited from sale into EU markets. That means that markets Scottish growers have developed for export over a number of years will in effect not be available to us from 1 January.
"We know officials at all levels of government in Scotland and the rest of the UK are well aware of the potential damage to the UK seed industry and have made representations about it."
Mr Gibson said: "To lose access to those markets established over the last 40 years will have a significant impact on our industry and for European markets as well, it's going to have a negative impact on their business as well."
He added: "Some businesses could suffer considerable financial hardship. It's too early to say at this moment in time but I think belt tightening will be in order for everyone."