Fructooligosaccharides are prebiotic sugars that are widely used in the production of functional foods, which can be produced enzymatically by the transfructosylation reaction of sucrose. This work aimed to optimize the production of an invertase with high transfructosylation activity from Aspergillus carbonarius PC-4 using pineapple crown as the inducer substrate and evaluate its biochemical properties. The culture medium was optimized using a Plackett–Burman experimental design and a central composite rotatable design, resulting in a maximum transfructosylation activity of 65.33 U/mL at 72 h of cultivation. The cultivation parameters were Yp/s = 1070.75 U/g and P_P = 2771.48 U/h, which showed an increase of 5.2-fold in the enzyme produced. The optimum temperature (50 °C) and pH (5.0) for the enzymatic activity were obtained by a CCR design. The enzyme showed a half-life of 60 min at 40 °C. In conclusion, the invertase produced from A. carbonarius PC-4 using agro-industrial waste (pineapple crown) and an inorganic nitrogen source (ammonium nitrate) exhibits high transfructosylation activity that can be used as a potential source for the production of fructooligosaccharides.