The attack caused "minor damage" to the ship, according to the Saudi-led, US -backed coalition battling the rebels.
The attack was "only a desperate attempt to influence the security of worldwide navigation. that will not affect economic activity or disruption of oil supply", Falih said Wednesday in a Tweet.
Saudi oil industry sources told Reuters news agency that oil operations and shipments were proceeding as normal and that security around facilities inside the kingdom had not been raised further.More news: Marine helicopter crew of 4 presumed dead after crash in California
The UN has described it as "one of the deadliest attacks" on minors in the country for years.
The 303,000-dwt Abqaiq (built 2002) was en route from Ras Tanura in Saudi Arabia to Ain Sukhna in Egypt when it was targeted.
A spokesman for the Saudi-led coalition said: "We take this report very seriously and it will be fully investigated as all reports of this nature are - using an internationally approved, independent process".
Yemen has been engulfed in a violent conflict between the government headed by Yemeni President Abd Rabbuh Mansur Hadi and the Houthi movement, also known as Ansar Allah.More news: AAA: Distracted Driving an Increasing Problem
The Houthis, who control most of northern Yemen, have launched missiles at Saudi Arabia, including the capital Riyadh, in the past few days.
Last week, Saudi air defences intercepted a flurry of missiles, and falling debris caused the first death in the capital Riyadh.
Saudi Arabia and its allies have repeatedly been accused of hitting civilians targets including hospitals and markets in their three-year campaign against the Huthis.
Medics and a civilian who saw the wreckage said the air strike had destroyed a house in the al-Hali district, where displaced civilians from other provinces were settled. Saudi Arabia accuses Iran of arming the Houthi militants as part of a proxy war. Tehran and the Houthis deny the allegation.More news: A life of struggle — Winnie Madikizela-Mandela