Assad cast his ballot at a polling station in a school in the al-Maliki neighbourhood, Xinhua reported.
The three candidates are al-Assad, former minister Hassan al-Nouri and lawmaker Maher Hajjar.
Syria's interior ministry said that more than 15 million registered voters are eligible to cast their ballots at 9,610 polling stations across Syria.
The polling stations will remain open from 7 a.m to 7 p.m.
The government has reportedly set up ballot boxes in shelters to allow thousands of displaced Syrians participate in the election.
The vote is taking place despite its rejection by the opposition and its Western backers, who have dismissed the process as a "farce".
Syrians living overseas cast their ballots last week.
Syrian nationals, mainly in Malaysia, China, South Korea, India, Indonesia, Lebanon, Venezuela, Jordan, Iran and Oman, voted at the Syrian embassies and consulates in these countries.
The election will be the first in half a century. Previously, there were only referendums to support Assad or his late father Hafez al-Assad, who was in office from 1971 to 2000.