The shortest war in history was between Britain and Zanzibar on August 27, 1896 - Apparently.
This brief conflict was sparked when Zanzibar's pro-British Sultan Hamad bin Thuwaini died, and the opposing faction installed a new Sultan, Khalid bin Bargash. The British, seeking to maintain their influence in the region, demanded Bargash's resignation. When he refused, they launched a naval attack, and Zanzibar surrendered after just 38 minutes of fighting. The Treaty of Zanzibar was signed soon after, making it the shortest war in recorded history.