The blast occurred at the 220,000 barrel per day Pembroke refinery on Thursday evening. A Chevron spokeswoman said the refinery remained fully operational on Friday.
Police said a fire had broken out after an explosion in a storage tank during maintenance. An adjacent storage tank was also damaged.
"I was in the back garden and I just heard a large explosion, looked around and I could see a fireball rising up into the sky," local resident Phil Horne told the BBC, adding that smoke billowed out for between 30 and 45 minutes.
The fire service said it sent 10 emergency vehicles to the scene and the ambulance service said it responded with three ambulances and an air ambulance.
"We will take every step possible to determine the series of events that led to this tragic incident," U.S.-based Chevron said.
Milford Haven, a nearby port which is home to two large liquefied natural gas terminals, said its shipping operations had not been affected.
Chevron put the refinery up for sale last year to lower its exposure to the refining business, echoing similar moves by rivals such as Royal Dutch Shell Plc and BP Plc. Falling oil demand in Europe has made it the least attractive location for refinery investment.
U.S. refiner Valero Energy Corp agreed in March to buy the refinery and other assets in a $730 million deal expected to close in the third quarter.
Valero was not available for comment on whether it would go ahead with the purchase.
Britain's Health & Safety Executive (HSE) regulator said it would be on site on Friday to begin an investigation in which the Environment Agency would also participate.
Concerns over refining safety have reverberated through the U.S. oil industry since an explosion at a BP refinery in Texas City in 2005, after which BP said safety shortcomings were common across the sector.
According to a HSE's enforcement database, the Pembroke plant had received one enforcement notice in recent years.
This criticized the plant for "failure to demonstrate the company had identified safety instrumented systems," though the HSE noted the enforcement notice had been complied with.
By comparison, four enforcement notices were issued to the Coryton refinery in southeast England, which was owned by BP before being sold to Swiss-based Petroplus Holdings AG, and three notices were given to Exxon Mobil Corp's Fawley refinery in southern England.