Grapes’ infection with the fungi Botrytis cinerea is one of the major causes of economic loss in the winemaking sector worldwide. The laccase activity of grapes is considered an appropriate indicator of this type of fungal infection, and enzymatic activity higher than 3 U/mL indicates a high risk of irreversibly damaged grape must due to enzymatic browning. This work describes a fast test for the measurement of laccase activity based on a dual optical and electrochemical detection method. A paper sensor impregnated with the enzymatic substrate dye 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) provides a semi-quantitative optical measurement. While the paper sensor can be used independently, when combined with a screen-printed electrode and amperometry measurements, it enables the quantitative detection of laccase activities down to 0.4 U/mL in only 5 min. The method was applied for monitoring the artificial infection of white, rosé, and red grapes with different strains of Botrytis cinerea. The results were confirmed by parallel analysis using the spectrophotometric method of laccase activity determination based on syringaldazine. The influence of the fungal strain and type of grape on laccase activity levels is reported. The demonstrated robustness, simplicity, and versatility of the developed method make it ideal for application on-site in the vineyard or at grape processing points.