The cabinet, at its weekly meeting, voiced "congratulations to President Erdogan of Turkey and the Turkish people on the success of the referendum regarding constitutional reforms," the official Saudi Press Agency reported.
The cabinet said it hoped the vote would contribute to "more development success across the country".
The 'Yes' camp won more than 51 percent in Sunday's referendum while the 'No' side got almost 49 percent, according to near-complete results released by Turkey's election authorities.
International observers said the referendum campaign was conducted on an 'unlevel playing field', while Mr Erdogan's opponents fear the result will hand him one-man rule.
Saudi Arabia and Turkey, two Sunni Muslim nations, have become increasingly close over the past year, sharing in particular a backing for the opposition in Syria's war.
Saudi King Salman hosted Mr Erdogan when he visited Riyadh to further strengthen ties in February.