The decision was made after the Argentina World Cup winner made an attempt to join Manchester United in the final weeks of the summer market.
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With skipper John McGinn on the bench, Ezri Konsa - rather than Martinez - took the armband for last night's Europa League win against Maccabi Tel Aviv.
"The first captain is John McGinn," Emery said via Birmingham Live. "We decided how we are, as well as managing the next captain.
"Usually, we have another captain, Emi Martinez, as second captain. But now, after speaking with him, I prefer to get him back.
"Konsa is the next one. Tyrone Mings, with Ollie Watkins too. Normally, we are managing it like that."