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 per cent in yesterday's referendum while the "No" side got almost 49 per cent, 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 Erdogan's opponents fear the result will hand him one-man rule.
Saudi King Salman hosted Erdogan when he visited Riyadh to further strengthen ties in February.