"We cannot wait, passively, for the possible impact," Greece's Citizens' Protection Minister Michalis Chrisochoidis said on a visit to the region of Evros on Friday.
"Our borders will remain inviolable."
His comments came as Turkey called on European countries to take responsibility for Afghan migrants, reports the BBC.
In a telephone conversation with Greek Prime Minister Kyriakos Mitsotakis, Turkey's President Recep Tayyip Erdogan said a sharp increase in people leaving Afghanistan could pose "a serious challenge for everyone".
"A new wave of migration is inevitable if the necessary measures are not taken in Afghanistan and in Iran," Mr Erdogan said.
The rapid takeover of Afghanistan by the Taliban, an Islamist militant group, has left some fearing for their lives and seeking to escape the country, often by any means necessary.
Mr Chrisochoidis said the crisis had created new "possibilities for migrant flows" into Europe.