Ismail Haniyeh’s office said the invitation was delivered by a visiting Russian diplomat.
Unlike the United States, Israel and the European Union, Russia does not view Hamas, the Islamist movement running the Palestinian enclave of Gaza, as a terrorist organization.
Hamas has not provided details on the date nor the agenda of trip.
Russian authorities have maintained high level contact with Hamas by receiving Hamiyeh himself several times.
Hamiyeh’s predecessor Khaled Mashaal also travelled frequently to Moscow.
A Hamas delegation, headed by deputy head of the political bureau, Mousa Abu Marzouk, visited Moscow in September.
The delegation met with Mikhail Bogdanov, Putin’s envoy to the Middle East and Africa, the Russian deputy foreign minister, and other foreign ministry officials.