Anthocyanins are often used in functional foods and beverages as colorants and nutraceuticals. However, these natural compounds may undergo chemical degradation during storage leading to color fading and loss of bioactivity. In particular, vitamin C (l-ascorbic acid) is known to accelerate anthocyanin degradation. In this study, the influence of various food-grade biopolymers on the physical and chemical stability of model beverages containing anthocyanin (0.025%), ascorbic acid (0 or 0.05%), and calcium salt (0 or 0.01%) was examined under accelerated conditions (40 °C for 7 days). Four biopolymers (1%) were examined for their potential to inhibit anthocyanin degradation: native whey protein; denatured whey protein; citrus pectin; and beet pectin. The physical stability was determined by measuring changes in absorbance, color, and visual appearance. Solutions containing anthocyanin and calcium salt (0 or 0.01%) were stable throughout storage, while those with added ascorbic acid were the least stable. The addition of biopolymers, particularly heat denatured whey protein, significantly enhanced the stability of the anthocyanin during storage. Fluorescence quenching studies showed that the anthocyanin may have formed complexes with the whey protein through hydrogen bonding that resulted in their enhanced stability in the presence of ascorbic acid. This study provides information that may improve the stability of anthocyanins in food and beverage systems.