The first mention of the village dates back to 1352, when it was mentioned as Conradi villa. In 1358 there was a parish church. To the north of the village on the Castle Hill there was a medieval fortress, which was the seat of the first owner of Kunratice, Hanus Jan Pancír. During the Hussite campaign in 1429, the fortress was probably destroyed, as it is no longer mentioned in later reports. The village was devastated by several disasters - the Thirty Years' War, peasant storms and a plague in which 60 people died. Therefore, a plague column was build in the village.
The Church of the Exaltation of the Holy Cross dates back to 1833. It was built near the road in the centre of the village, on the site of an older church. The three-aisled building with a front tower is built in the Empire style. In the early 1980s Kunratice was annexed to Cvikov, but in the 1990s it became independent again.
There are several climbing terrains in the vicinity of Kunratice, such as the Hollow Stone or the Rock of Death.