Saudi billionaire Prince Alwaleed bin Talal has warned that the kingdom's oil-dependent economy is increasingly vulnerable to rising U.S. energy production, breaking ranks with oil officials in Riyadh who have played down its impact.

In an open letter dated May 13 addressed to Saudi Oil Minister Ali al-Naimi and several other ministers, a link to which was published Sunday on Prince Alwaleed's Twitter account, he warned that the boom in U.S. shale oil and gas will reduce demand for crude from members of the Organization of...