Born in Las Heras, Mendoza, Fragapane joined Boca Juniors' youth setup in 2005, aged 12,[2] after impressing in a trial.

[3] He played his first match as a professional on 1 March 2012, coming on as a late substitute in a 2–0 home success over Central Córdoba de Rosario, for the season's Copa Argentina.

[4] Fragapane played regularly with the reserve side during the following seasons, and made his Primera División debut on 8 December 2013, again from the bench in a 1–1 home draw against Gimnasia La Plata.

On 12 July 2014 Fragapane moved abroad for the first time in his career, joining Spanish Segunda División B side Elche CF Ilicitano on loan, with a buyout clause.

[6] On 6 December he made his debut with the main squad, replacing Coro in a 0–2 La Liga home loss against Atlético Madrid.