City investigators found Carranza took his wife to see the show using tickets designated for employees of the Department of Education.
The NYC Conflicts of Interest Board made the ruling on Thursday.
The special tickets cost only $10 as part of a partnership with the education department in 2019.
The board found that "in using this ticket for his wife, the chancellor used his city possession to benefit his wife."
He has been ordered to pay a fine of $1,000 to the board.
Carranza resigned as chancellor in March. He was replaced by former Bronx Executive Superintendent Meisha Porter.
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