"We do not want a war in the region... But we won't hesitate to deal with any threat to our people, our sovereignty, our territorial integrity and our vital interests," Prince Mohammed said in excerpts published early Sunday of an interview to pan-Arab daily Asharq al-Awsat.
The attacks on Thursday on two tankers in the Gulf of Oman sent crude prices soaring amid a tense standoff between Iran and the US.
The Japanese-owned Kokuka Courageous was carrying highly flammable methanol through the Gulf of Oman when it was rocked by explosions, causing a blaze that was quickly extinguished.
US President Donald Trump said the twin attack, which also targeted a tanker owned by Oslo-listed company Frontline, had Iran "written all over it".
Tehran has vehemently denied any involvement.
Saudi Arabia, a close US ally, is a bitter regional rival of Iran.
Iran has repeatedly warned in the past that it could block the strategic Hormuz Strait in a relatively low-tech, high-impact countermeasure to any attack by the United States.
Doing so would disrupt oil tankers travelling out of the Gulf region to the Indian Ocean and global export routes.