This study prepared a green, edible sodium alginate/starch/wormwood extract (SA-St-A) composite film. Natural wormwood extract (Artemisia extract, A) was added as an antimicrobial agent to the composite matrix of sodium alginate (SA) and starch (St), and the structure and properties of the resulting films were characterized. The results indicated that, with an increase in A concentration, the mechanical properties and thermal stability of the composite films gradually improved, while their light-blocking performance also increased. The composite film with a 2% A concentration showed the best overall performance. The contact angle of the films increased with the A concentration, and the water content decreased, indicating that the hydrophilicity of the films decreased with the addition of A, with the lowest hydrophilicity observed in the 2% A concentration film. The SA-St-A composite films exhibited good antibacterial activity against Staphylococcus aureus (S. aureus), and their antibacterial activity strengthened as the A concentration increased, with the best antibacterial effect observed at the 2% concentration. Finally, the preservative effect of the prepared composite films on cherries stored at 4 °C for 15 days was investigated. The results showed that the SA-St-A composite film effectively extended the shelf life of cherries, delaying the loss of weight, hardness, and soluble solid content. Therefore, the SA-St-A composite film has broad prospects for application in fruit and vegetable preservation, providing insights for expanding the use of A and improving the preservation of fruits and vegetables.