"If they deal a blow to Greece, then they should know the the migrants will get papers to go to Berlin," Kammenos told a meeting of his right-wing party, Independent Greeks.
He also said that if some of the refugees were members of the terrorist group Isis, it would be Europe's fault because of its position on Greece's economic problems.
Kammenos' comments echoed similar statements made by Greek vice interior minister Giannis Panousis just a week ago.
In response, the German police union suggested Greece be excluded from the Schengen area of 26 European countries that do not require passport and border control of one another for travel across their borders.
Greek foreign minister Nikos Kotzias had said on Friday at a meeting of EU foreign ministers that if Greece were to collapse economically, it would become a gateway for "millions of immigrants and thousands of jihadists".
The defence minister's most recent threats came on the heels of a Monday meeting in Brussels of Eurozone finance ministers to discuss the next steps in dealing with Greece's crisis.
A four-month extension of Greece's bailout programme was approved last month to run until the end of June. In return, Greece must implement certain reforms.
Greece's debt amounts to €320 billion - equivalent to 175 percent of its annual economic output. By the end of March, the country must meet obligations amounting to €6.85 billion.