Zelenskiy wrote that the primary topics of discussion would be Ukraine's Peace Formula framework for ending Russia's invasion as well as the return of captives and deported people.
The Saudi state news agency confirmed in a statement that Zelenskiy had arrived in the kingdom.
Ukraine has held several multilateral meetings to discuss the peace formula with representatives from dozens of countries.
Ukraine hopes to hold a peace summit in Switzerland involving the leaders of those countries in the northern hemisphere spring.
"Now we are very close to holding the first peace summit and we count on continued active support from Saudi Arabia," Zelenskiy wrote in his statement.
Saudi Arabia has previously acted as a mediator in prisoner swaps between Ukraine and Russia.
Zelenskiy said he was sure his meeting on Tuesday would "bring results" in this regard.
His trip comes as Ukrainian forces were slowly being pushed back in the country's east.
Russia has gained the initiative due to its big advantage in troop numbers and weapon supplies, military analysts say, as Ukraine waits for news of new provisions from its allies.
The Ukrainian military said on Tuesday it withdrew its forces from two more villages near Avdiivka in the eastern Donetsk region following intense overnight fighting.
Ukrainian troops have pulled back from Sieverne and Stepove, army spokesman Dmytro Lykhovyi said.
The two villages had a population of about 100 people in total before the full-scale invasion, he said.
The state-run Saudi Press Agency said Zelenskiy arrived at Riyadh's King Khalid International Airport and was met by government officials.
Later footage showed Zelenskiy along with top officials in his government meeting with a smiling Prince Mohammed.
Also on hand was Saudi Energy Minister Prince Abdulaziz.
Footage showed the prince and Zelenskiy, both of whom speak English, talking among themselves without translators in a vast greeting hall at a palace as other officials sat nearby.
In May, Zelenskyy travelled to Saudi Arabia for a meeting of Arab leaders and also met then with Crown Prince Mohammed.
Saudi Arabia, the United Arab Emirates and Qatar - all neighbours on the Arabian Peninsula - have been involved in prisoner exchanges since the war broke out in 2022.
Germany, the United Kingdom and other European countries said on Tuesday they had no plans to send ground troops to Ukraine, after France hinted at the possibility, and the Kremlin warned that any such move would inevitably lead to conflict between Russia and NATO.
French President Emmanuel Macron had said on Monday at a hastily convened meeting of European leaders in Paris that no options should be excluded in seeking to avert a Russian victory in Ukraine, although he stressed there was no consensus at this stage.
However, Germany, the UK, Spain, Poland and the Czech Republic distanced themselves from any suggestion they might commit ground troops to the Ukraine war, now in its third year.
"...There will be no ground troops, no soldiers on Ukrainian soil sent there by European countries or NATO states," German Chancellor Olaf Scholz said on Tuesday.
with AP
