Brent crude futures were up $1.91, or 3.18%, at $61.88 a barrel by 1039 GMT, having risen as much as 4.45% to $62.64.
U.S. West Texas Intermediate crude futures were up $1.42, or 2.78%, at $52.56 a barrel. WTI earlier rose as much as 3.85% to $53.11.
The attack left one ablaze and adrift as sailors were evacuated from both vessels and the U.S. Navy rushed to assist amid heightened tensions between Washington and Tehran.
One of the tankers carried oil bound for Japan, whose Prime Minister Shinzo Abe was wrapping up a high-stakes visit in Tehran that sought to ease tensions between Iran and the United States.
A third of all oil traded by sea passes through the strait, which is the narrow mouth of the Persian Gulf.
The latest incident comes after the U.S. alleged that Iran used mines to attack four oil tankers off the nearby Emirati port of Fujairah last month.
Iran has denied being involved, but it comes as Iranian-backed rebels in Yemen also have launched missile and drone attacks on Saudi Arabia.
Dryad Global, a maritime intelligence firm, preliminarily identified one of the vessels involved as the MT Front Altair, a Marshall Islands-flagged crude oil tanker. The vessel was "on fire and adrift," Dryad added. It did not offer a cause for the incident or mention the second ship.
The firm that operates the Front Altair told The Associated Press that an explosion was the cause of the fire onboard. International Tanker Management declined to comment, but said its crew of 23 is safe after being evacuated by the nearby Hyundai Dubai vessel.
The second vessel was identified as the Kokuka Courageous. BSM Ship Management said it sustained hull damage and 21 sailors had been evacuated, with one suffering minor injuries.
The timing of Thursday's reported attack was especially sensitive as Abe's high-stakes diplomacy mission was underway in Iran. On Wednesday, after talks with Iranian President Hassan Rouhani, Abe warned that any "accidental conflict" that could be sparked amid the heightened U.S.-Iran tensions must be avoided.
The Associated Press contributed to this article.