The Morshansk Museum was founded in 1918 by self-taught archaeologist, artist, and local historian Pyotr Petrovich Ivanov. It was located in a former upper clothing store owned by the Kaverin merchants, one of the best buildings in the city. Since 1912, Ivanov had been striving to open a museum in Morshansk, but his dream was realized only six years later. The official date of the museum's founding is April 13, 1918, when the district executive committee of Morshansk adopted a resolution for its establishment. The October Revolution facilitated the transfer of part of the property from noble estates to the people's historical and archaeological museum, which became the first district museum opened in the first year of Soviet power. In 1925, the building was fully transferred to the museum.

Ivanov created the museum based on his collection, which he had gathered for 15 years. Initially, the funds included over 2000 items from his personal collection and 144 items donated by other individuals and organizations.

Since 1925, when the museum occupied the entire building, the collections were divided into departments: archaeology, antique weapons, ethnography, numismatics, church-historical artifacts, and industry. The initial exhibition had a cabinet of curiosities character, and the museum's profile was historical and archaeological. In 1926, the art department opened, where works of art were donated by city residents. The inhabitants of the city and surrounding villages actively participated in the development of the museum.

Since 1941, the museum became a local history museum. In 1950, staff began collecting ethnographic material in scientific research expeditions.

In 1993, the Morshansk Museum received the status of a historical and art museum. Museum staff conduct educational events dedicated to the Victory in the Great Patriotic War for schoolchildren. Events titled 'Museum and Orthodox Culture' are also organized.

The museum has a historical and cultural club 'Olympus', created in 2006 at the initiative of the city’s culture department.

In 2014, the correspondence of the museum's founder Pyotr Petrovich Ivanov was published in the form of a collection of documents from the archival collection titled 'I Always Do Not Leave Letters Without Answers...'.