The strikes hit areas north of Yemen’s port city of Hodeidah, Saudi state TV reported.
The attacks come six days after the Khurai and Abqaiq oil plants were damaged in an operation that Houthi rebels claimed responsibility for and which temporarily halved the kingdom’s oil production.
On Friday morning local time, Saudi-run Ekhbariya TV said the coalition, which has the support of the US and the UK, had struck “legitimate military targets”.
There was no immediate confirmation of the strikes, or which coalition members were involved. Broadcasters urged civilians to stay away from the areas that had been hit.
The reported operation came two days after officials in Saudi Arabia held a press conference to display debris from drones and cruise missiles, which they claimed proved Iran was involved in the oil attack. Iran has repeatedly denied it was involved and has vowed to defend itself.
Earlier, the US said it was starting the task of building a coalition to deter purported Iranian threats. US secretary of state Mike Pompeo has said that Mr Trump, who has ordered more sanctions on Iran, wanted a peaceful solution to the crisis.
Mr Pompeo was speaking after holding talks with Saudi and Emirati leaders over the strike that Washington and Riyadh have blamed on Tehran. “We are here to build out a coalition aimed at achieving peace and a peaceful resolution,” said Mr Pompeo.
Donald Trump on Iran: ‘I don’t want a war but US is more prepared than any country’
“That’s my mission, that’s what President Trump certainly wants me to work to achieve and I hope that the Islamic Republic of Iran sees it that way.”
Mr Pompeo did not provide details about the coalition. The United States has, however, been trying to create a global maritime security alliance since attacks on oil tankers in Gulf waters, which Washington also blamed on Iran.
The UAE, Saudi Arabia, Britain and Bahrain have said they will participate. Iraq said it would not join, and most European countries have been reluctant to sign up for fear of stoking regional tensions.
The military operation against Houthi rebels has resulted in thousands of civilian casualties and created a massive humanitarian crisis in one of the poorest countries in the world.
Mr Trump has overruled efforts by politicians in the congress to end military support for Saudi Arabia, which the president considers a major ally. Critics of Saudi Arabia accuse it of widespread human rights abuses, and of the 2018 murder of journalist Jamal Khashoggi.
Additional reporting by Reuters