The Saudi statement noted that the trainer was killed in the course of a routine activity. It did not say whether he was a member of the military or a civilian.
A Saudi trainee pilot was also injured in the crash.
Investigators have been trying to determine the cause of the incident.
US Defense Secretary James Mattis in March acknowledged that Washington had been involved in managing Saudi Arabia’s airstrikes in Yemen.
Mattis also admitted that the US had been involved in mid-air refueling of Saudi warplanes, claiming that the operation could help minimize civilian casualties in the war-torn country.
The Pentagon chief’s comments contradict America’s long-standing claims of a very limited, non-combat engagement in the Saudi war on Yemen.
The US has previously said that its assistance to the Saudi-led coalition is limited to aircraft refueling, logistics and general intelligence sharing.
The White House also claims that its involvement has nothing to do with the civilian death toll in the Arab country.
In March, the administration of US President Donald Trump approved weapons sales to Saudi Arabia totaling more than $1 billion, despite growing pressure from rights groups to halt arms deals between the West and Riyadh.
Amnesty International has slammed the United States, Britain and France for their continued arms sales to Saudi Arabia and the United Arab Emirates. The UK-based rights group said the arms sales have been an "enormous harm to Yemeni civilians" over the course of the war.
This comes as The Mail reported in November last year that the British Army was secretly training Saudi Arabian soldiers to fight in Yemen. The training, codenamed Operation Crossways, was disclosed after the UK Army mistakenly released photos and a mission summary on 2 Scots’ Facebook page.
The Saudi military aggression against Yemen has so far killed some 15,000 and put millions of others on the verge of famine. It has also caused a deadly outbreak of cholera.
Some Arab monarchies of the Persian Gulf region also host thousands of American military personnel.
The United States has also trained militants in Jordan for operations in Syria.
Source: Press TV