The results of this study provide overall information on the verification of the effect of applying two different mulching materials of an organic origin to the soil surface in the area between rows of grape vines in vineyards on selected physical and chemical properties of the soil and, at the same time, on the yield and quality parameters of the grape vines (Vitis vinifera L.). During the period under study, 2018–2020, the effect of shredded cereal straw (CS) and compost from garden waste (CO) was investigated. The control variant (CWC) was left without any cover and was regularly cultivated with a coulter cultivator to a depth of 60 mm. During the experiments, meteorological data were monitored and recorded along with soil temperature and soil moisture for each variant. The results show that the lowest temperature was measured for the straw cover variant (11.10–11.87 °C), while the highest soil temperature was measured for compost (11.93–13.16 °C). Under the straw, the moisture level in the soil was higher compared to the other variants, and there was a gradual increase (of 3%) in soil bulk density values compared to the baseline. By contrast, the compost variant showed a decrease (of 1%) in bulk density values. The differences in nutrient content were slight among the variants. The only statistically significant difference was identified for the compost variant with respect to the content of total nitrogen and phosphorus. Further results demonstrated a positive effect of both mulch material variants on grape yield, which was 6–19% higher in the variants with a cover layer. In addition, the use of mulch also had a positive effect on grape quality. For example, the sugar content—one of the main quality parameters—increased by 1–7% due to the mulch layer. Based on these results, the use of mulching materials can be recommended for areas with low total rainfall during the growing season, as well as when growing varieties with irregular yields and uneven grape quality.