According to foreign ministry officials, Saudi Arabia – which sits on the world’s largest oil reserves – is expected to sign a cooperation deal with Russia in the oil and gas sectors
Russia is the biggest exporter of oil outside the Organisation of Petroleum Exporting Countries (OPEC).
The official visit is seen a positive step between the two countries as relations had recently soured when Moscow accused Riyadh of permitting Saudi funding of Chechen separatists.
But Russia and Saudi Arabia say they are united on security matters after major bombing attacks in May in both Saudi Arabia and Chechnya.
A Russian diplomat in Riyadh told the French news agency AFP that the crown prince was expected to convey to Russian President Vladmir Putin, "the Kingdom’s position towards the question of Chechnya and the war there."