He first trained locally with Francesco Antonio Camuncoli, then Giovanni Battista Frulli and the engraver Francesco Rosaspina in Bologna, then moved to Rome to the circle of Canova and Minardi.
He also painted portraits for Professor Bonaventura Corti, Giuseppe Garofali, Doctor Giovanni Battista Spallanzani, Francesco IV, and Napoleon I. Rocco engraved his designs for a History of Scandiano.
His portrait of Conte Governatore Ippolito Malaguzzi Valeri was reproduced in an engraving by Delfino Delfini.
When Camuncoli died in 1831, Minghetti served, until his death, as director of the School of Fine Arts in Reggio Emilia.
Among the students at the School while he was director were Alfonso and Gaetano Chierici; Carlo Zatti; Antonio Fontanesi, Domenico Pellisi (Pellizzi); Giuseppe Ugolini; Carlo Raimondi; Paolo Aleotti; Pio Canossini; Romualdo Belloli (engraver); and Del Rio (sculptor).