The Svyato-Voznesenskiy Kremenskoy Monastery was built several kilometres from Kremenskaya village on the bank of the Don river in 1693. The founder of the Kremenskoy Monaster was hieromonch Nikanor. The Kremenskoy Monastery is considered as one of the ancient monasteries of the Don Cossack Army. At first, the old chapel was given to the Svyato-Voznesenskiy Kremenskoy Monastery and then the monks obtained a permit from Peter the First for its further construction. However, soon the chapel was burnt. Its ash was dispersed across the Don river. In 1711 monk Kapiton built a hermitage and in1712 father superior Nikonor began the construction of the church in honor of Ascension. The construction was finished in 1716, and the church was sanctified.
The Monastery saw a great number of different events. By the beginning of the 20th century there were 47 novitiates and 25 monks in the monastery.
During the Great Patriotic War the military base was placed in the Svyato-Voznesenskiy Kremenskoy Monastery. That time one of the soldiers found a healing spring. Till the year of 1967 the building of the monastery was used as a psychiatric hospital.
The new story of the monastery started only in 1992 when the citizens of Frolovo helped to recover the Svyato-Voznesenskiy Monastery. Nowadays, the monastery possesses about 498 hectares of land including arable lands and pastures.