The President of Russia will take part in the official opening ceremony of the Sangtuda hydroelectric power station.
There will also be high-level Russia-Tajikistan talks.
During the visit to Tajikistan, Mr Medvedev will meet with Pakistani President Asif Ali Zardari, and take part in a four-way meeting with Emomali Rahmon, Asif Ali Zardari and Afghan President Hamid Karzai.