The extraction of date syrup produces a large quantity of by-product known as date press cake (DPC). This study aimed to utilize valuable ingredients of the DPC by adding 0 (Control), 2, 4, and 6% (g/100 g) of its powder to drinkable yogurt before fermentation. The physicochemical properties, texture profile, and sensory evaluation of the treated DPC-based drinkable yogurt (DPC drinkable yogurt) were measured after fermentation and 5, 10, and 15 days of storage at 4 °C. The modeling of the most critical quality attributes, i.e., pH, acidity, syneresis, water holding capacity (WHC), viscosity, and color difference (ΔE), was conducted to predict their values based on the DPC percentage and storage period. The DPC drinkable yogurt’s total solids, protein, and fat ranged between 11.19–11.83, 3.10–3.42, and 2.26–2.34%, respectively. Adding 2–6% DPC slightly increased the pH of DPC drinkable yogurt and decreased its acidity (p > 0.05) during storage. Increasing the DPC percent in DPC drinkable yogurt decreased the syneresis value, and WHC increased during storage. The color parameters and viscosity of DPC drinkable yogurt recorded the highest value at the end of the storage period for all treatments and increased steadily with the increase in DPC. The evaluation of the prediction models indicated that the predicted values were close to the actual experimental values for pH (R2 = 0.779), acidity (R2 = 0.973), syneresis (R2 = 0.961), WHC (R2 = 0.989), viscosity (R2 = 0.99), L* (R2 = 0.919), a* (R2 = 0.995), b* (R2 = 0.922), and ΔE (R2 = 0.921). The textural analysis indicated that increasing the concentration of DPC in the DPC drinkable yogurt increased hardness (g), springiness, cohesiveness, and gumminess and decreased adhesiveness and resilience during cold storage. The evaluation of sensory acceptance during the cold storage of the DPC drinkable yogurt was conducted by 30 expert panelists. Each panelist received four cups of 10 mL drinkable yogurt treatments at 5–10 °C. The evaluation results indicated that adding 2% of DPC was closest in overall sensory acceptability to the control sample (p < 0.05). This study revealed the potential use of DPC in drinkable yogurt as a natural, functional, and low-cost ingredient to improve the fiber content, physicochemical properties, and overall acceptability. Therefore, the fermented DPC-based yogurt drink has the potency to be a practical, value-added, and novel alternative to dairy-based yogurt.