Born in Cittadella, Veneto, Minesso started his career at Vicenza. Minesso made his Serie B debut on 10 May 2008, replacing winger Davide Matteini in the second half. In that match, Vicenza won Frosinone 2–1. Minesso also played for Vicenza's Primavera under-20 team from 2007 to 2010 after promoted from its Allievi Nazionali under-17 team. Minesso failed to play any game for the first team in 2009–10 Serie B but also only played 4 times for Primavera that season.
On 24 June 2010, five days before the closure of 2009–10 financial year of "A.C. Chievo-Verona s.r.l." and "Vicenza Calcio S.p.A.", Minesso joined Serie A club Chievo, while Amedeo Benedetti joined the opposite side. Both players were "valued" for €2 million. Co-currently both clubs bought back 50% registration rights for €1M as part of co-ownership deal. As youth product usually did not had a value as "intangible asset", both clubs had a selling profit On 30 June 2010, Chievo had a positive shareholder equity of €687,180, thus no need to recapitalisation. However, Minesso was part of the "intangible asset" of Chievo which "worth" €2 million at that time, plus Daniele Rosania "worth" €1 million. Vicenza also swapped players with Ascoli and Cesena before the closure of the financial year. Minesso did not remain in Verona, another city of Veneto. Instead Minesso immediately returned to the city of Vicenza but Minesso only made 5 league appearances in 2010–11 Serie B, as number 9 of the team. On 7 January 2011, Minesso joined Lega Pro Prima Divisione club Andria, re-joining team-mate Mattia Evangelisti. Minesso played 14 times in 2010–11 Lega Pro Prima Divisione, but only 8 starts.
Vicenza return
In June 2011 both Benedetti and Minesso returned to their mother clubs for the same price. Again, Chievo had a positive equity of €679,516 and player asset of €20,156,304, but composited with players such as Benedetti and Alessandro Bassoli On Vicenza side, the club also swapped Tonelli with Cesena before the closure of 2010–11 financial year. As Minesso had a "value" of €2 million in accounting, Vicenza failed to find a new club to buy him. Instead Minesso's loan was renewed on 16 July 2011 After Vicenza relegated, Minesso returned to the club and took part in pre-season. He was confirmed as part of the squad despite Vicenza was re-admitted to 2012–13 Serie B on 23 August after the expel of Lecce. He wore no.15 shirt.
Cittadella
On 25 January 2013, Minesso left for another Veneto and Serie B club Cittadella, which Tommaso Bellazzini moved to opposite direction. On 1 July 2013 Cittadella signed Minesso outright.
