Smart packaging is a packaging system with embedded sensor or indicator technology, which provides information on the quality of the product, especially perishable foods such as goat milk. One application of smart packaging is to use a time-temperature bioindicator. The purpose of this study was to determine the quality of fresh goat milk during storage at freezing temperatures (−20 ± 2°C) for 31 days and room temperature (25 ± 3°C) for 24 hours using a time-temperature indicator by utilizing a natural dye betacyanin. The method used was descriptive analysis, and the data obtained were processed using the correlation regression test. The samples were observed at freezing temperature every 24 hours and room temperature at 0, 1, 2, 3, 4, 5, 6, 8, 10, and 24 hours. The observation criteria consisted of changes in bioindicator color, milk pH, and total microbes. The results showed that color changes of the bioindicator film at room temperature were more noticeable than at freezing temperature. Based on changes in color of the bioindicator at room temperature, the sample was safe for consumption until the 5th hour with pH 6.51, and the biofilm color characteristics were L∗ = 82.49, a∗ = 21.46, and b∗ = −7.33, but the total number of microbes did not fulfil Indonesian National Standard at the 24th hour, i.e., 1.36 × 106 CFU/ml. At freezing temperatures, fresh goat milk was still safe for consumption until the 31st day with pH 6.51 and total microbe of 1.89 × 105 CFU/ml, and the biofilm color characteristics were L∗ = 80.52, a∗ = 24.15, and b∗ = −7.91. The results of this study concluded that the milk expiration limit based on the betacyanin indicator was 5 hours at room temperature and 31 days at freezing temperature.