In 1826, Savva Vasilyevich Morozov, the founder of a famous merchant dynasty, acquired a plot of land in the Rogozhskaya part of Moscow, in what is now Shelaputinsky Lane, where there were stone buildings and a garden. Over time, his estate expanded by acquiring neighboring properties, and next to the mansion, Morozov built a weaving factory. Although it was not the largest among the Morozov manufactories, in 1846, it employed 250 people, producing fabrics worth 40 thousand rubles.

Savva Vasilyevich Morozov died in 1862 and was buried at the Rogozhskoye Old Believer Cemetery, as the Morozov family adhered to Old Believer faith. By his will, the factory passed to his grandson David Abramovich, the son of the prematurely deceased Abram Savich.

David Abramovich decided to close the factory in Shelaputinsky Lane due to its low profitability. In 1887, he received permission from the city authorities to reconstruct the factory building to house a shelter for 150 people, intended to assist poor elderly and sick individuals of both genders and all classes. He allocated a significant sum of 500 thousand rubles for this purpose. Of this, 200 thousand were spent on construction according to the project by architect M. I. Nikiforov, while the remaining 300 thousand were deposited in the bank as an endowment to support the shelter. A church of the same faith was built next to the shelter in honor of Saints Fyodor and his sons David and Konstantin. After David Abramovich's death, the church became Greek Orthodox.

The shelter opened in 1891. In the following years, it was partially reconstructed and expanded according to the projects of architects V. G. Sretensky and A. M. Kalmykov in 1894 and 1905. Many members of the Morozov family participated in the development of the institution, and the number of places in the shelter increased to 243.

After the revolution, the Morozov shelter was transformed into a nursing home, and later the building was renovated and a maternity hospital was opened, named after Clara Zetkin. This became one of the best medical institutions in Moscow. In 1945, it was visited by Clementine Churchill, who left a note in the 'Golden Book' of the maternity hospital: 'If I were to have a child again, I would like to entrust its fate to this institution.'

In the late 1980s, the maternity hospital was closed, and the building was slated for major repairs. However, since then, despite numerous investment contracts, restoration work was not carried out until 2016.

In April 2016, Mosgorheritage approved acts of the State Historical and Cultural Expertise for works on the preservation and adaptation of the cultural heritage monument. In April 2018, emergency works were carried out.