The newspaper, quoting senior US officials, said the June 20 attack had degraded the ability of Iran's paramilitary force to target shipping in the Gulf.
It said Iran was still trying to recover information and restart military communications networks and other systems knocked offline.
The Times said the cyberstrike was the latest in an ongoing cyberconflict between the United States and Iran.
It said the cyberattack went ahead after President Donald Trump had called off a retaliatory military airstrike against Iran for shooting down a US drone.
The newspaper said the White House viewed the cyberattack as a proportional response to the destruction of the unmanned drone.
It said the database targeted in the attack was used by the Guards to choose which tankers to target.
No tankers have been targeted since the June 20 operation although Iran did seize a British oil tanker after one of its vessels was detained, the Times said.