The 27-nation bloc has condemned Niger's junta for ousting Bazoum, a key Western partner in the jihadist-hit region.
The EU said it had adopted a legal framework under which it can now "sanction individuals and entities responsible for actions that threaten the peace, stability and security of Niger."
EU's foreign policy chief said the move "sends a clear message — military coups bear costs."
The Western economic bloc has already suspended security cooperation and financial support with Niger following the military takeover.
Former colonial power France is in the process of pulling out its 1,500-strong military deployment to the Sahel country after a demand from Niger's new rulers.
A relative told AFP on Sunday that Bazoum is with his family and is doing well, after claims by the country's new military rulers this week that he had tried to escape.
Since he was toppled by the military, Bazoum has refused to resign and has been held at his residence in the heart of the presidential palace along with his wife and son.
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