The USS Boxer, an amphibious assault ship, shot down the drone one month after Iran shot down a U.S. drone near the Iranian border.
Trump said the Iranian drone came about 1,000 yards away from the USS Boxer and ignored calls to stand down.
"The drone was immediately destroyed," Trump said during remarks in the East Room of the White House. "This is the latest of many provocative and hostile actions by Iran against vessels operating in international waters.
"The United States reserves the right to defend our personnel, our facilities and interests, and calls on all nations to condemn Iran's attempts to disrupt freedom of navigation and global commerce."
Last month, the Pentagon announced it was sending 1,000 additional troops to the Middle East to counter what it described as Iranian aggression.
Tensions between the United States and Iran have risen for months, and the conflict deepened after an attack on two tankers in the Gulf of Oman the United States blamed on Tehran. Tensions first began to escalate following the Trump administration pulling out of the 2015 nuclear deal, citing it was "defective at its core."