One of most beautiful monastery complex is situated on a forested rocky mountain called Shireet Ulaan, which elevated in 2300 meters above sea level.

The monastery was built in 1654 by Saint Zanabazar who was a great sculptor and one of the biggest representatives of Buddhism in Mongolia. Upon his return in 1651 from his first trip to Tibet he had a small walled stone meditation hut built here. 1653, he visited Erdenezuu, founded by his great grandfather, and appeared before a convocation of khalkha nobility. While there he prevailed upon his followers to build temple and retreat at Shireet Ulaan Uul in his own personal use. Later it became worship where many of his famous artworks were created; including five transcendent Buddha's now located in the Zanabazar Fine Art Museum and Choijim Lama Musuem. Zanabazar also reportedly designed his Soyombo Alphabet while his residing here. During Zanabazar's lifetime retreat was called Bayasgalant Aglag Oron (Happy Secluded Place).

After his death it became Tuvkhun Monastery, the name which it is known today. The small temple was heavily damaged by communists during the upheavals of the late 1930s. During the summer of 1997 extensive ceremonies were performed here and new statue of deity Gombo Makhagal (Mahakala) was placed in top of refurbished and consecrated. Several monks live at the monastery full time.