The history of the hospital at 27 Leninsky Prospekt, now known as the Central Clinical Hospital of Saint Alexius, Metropolitan of Moscow, begins in 1900. At that time, the Moscow City Duma allocated a plot of land on Kaluzhskaya Street, opposite the Neskuchny Garden, for the construction of a hospital and almshouse complex. The funds for the construction were bequeathed by Alexandra Ksenofontovna Medvednikova, a well-known philanthropist and merchant widow. Ivan Loginovich and Alexandra Ksenofontovna Medvednikova came from an ancient Irkutsk merchant family but spent most of their lives in Moscow.

According to A.K. Medvednikova's will, who passed away in 1899, two-thirds of her capital was bequeathed to Moscow for charitable purposes. With this money, a gymnasium was built on Starokonyushenny Lane and a shelter for epileptics near Kanatchikova Dacha, but the majority of the funds were directed towards the construction of a hospital for incurable patients of the Christian faith and an almshouse.

The complex was built in 1902-1903 according to the design of academic architect Sergey Ustinovich Solovyov. Along Bolshaya Kaluzhskaya Street, two large buildings were located: the almshouse, with the church of the Tikhvin Icon of the Mother of God, and the hospital, with the church of the Kozelshchanskaya Icon of the Mother of God (now Saint Alexius). In the depths of the territory, buildings with apartments for doctors and staff, utility buildings, an icehouse, and a chapel were constructed. All buildings were executed in the neo-Russian style, and the architecture of the house churches shows a noticeable influence of 17th-century Rostov temple architecture. The interior paintings of the churches were created by the workshop of the Pashkov brothers, while the mosaic panels and tiles on the facades were made in the workshops of the Stroganov School.

The hospital and almshouse were equipped with modern facilities: plumbing, sewage, electric lighting, ventilation, and a steam heating system. The hospital accommodated 150 people, while the almshouse housed 60. Sewing and bookbinding workshops were organized for patients, as well as a library. A school was provided for children in the hospital.

The complex of charitable institutions named after Ivan and Alexandra Medvednikov was solemnly opened in December 1903 in the presence of Grand Duke Sergei Alexandrovich and Grand Duchess Elizabeth Feodorovna. In 1908, with funds bequeathed by Alexandra Karpovna Rakhmanova, another almshouse was built with a separate entrance from Kaluzhskaya Street. The project was also developed by architect S.U. Solovyov.

During the Soviet era, the almshouses were abolished, and patients were placed in their buildings. The house churches and chapel were closed shortly after the revolution and adapted for hospital needs. In 1924, the Medvednikov Hospital became the 5th City Clinical Hospital. In 1992, it was renamed the Central Clinical Hospital of Saint Alexius, Metropolitan of the Moscow Russian Orthodox Church. The churches were restored and returned to the believers.