ATHENS—A Greek prosecutor raided the offices of the wife of Greece’s central bank governor Thursday as part of a continuing investigation into business she has done with a state entity, officials said, in a probe that may heighten tension between the top bank official and the left-wing government.

Lina Nikolopoulou-Stournaras, the wife of central bank Governor Yannis Stournaras and owner of an communications company specializing in the medical sector, is under investigation from Greek authorities for business she has done...