Al-Sudani will depart Iraq on October 9, meeting with Putin on October 10 and will hold work meetings on October 11, the government source said.
Iraqi state media last month reported al-Sudani would travel to Moscow to discuss cooperation between the two countries in the economic and political fields.
Iraq and Russia have had bilateral relations for decades. Cooperation between Baghdad and Moscow is primarily in the fields of energy, military and security.
Baghdad hosted Russian Foreign Minister Sergei Lavrov in February, when he led a delegation for representatives of Russian companies.
Both sides had then discussed food security and ways for Baghdad to handle payments to Russia in light of global sanctions imposed on Moscow after Russia attacked Ukraine.
Major Russian oil companies such as Gazprom Neft and Lukoil are among those working in Iraq, mainly in the oil-rich south.
In his visit earlier this year, Lavrov had stated Russian companies had “huge investments in Iraq that have reached $13 billion”.
Iraq is the second-largest producer of crude oil in OPEC after Saudi Arabia.