The Pentagon said the helicopter was shut down near the coast of Oman.
The EU alleged that Mr Akbarzadeh threatened drone and missile attacks against vessels passing through the strait.
The institutions made this known in a joint statement on Friday.
President Donald Trump threatened that the United States “would have to blow up” Oman should the country partner with Iran on the control of the Strait of Hormuz.
The United States and Iran again exchanged attacks near the Strait of Hormuz early on Thursday amid a ceasefire and ongoing negotiations on ending the war.
The U.S. said it targeted missile launch facilities and Iranian boats allegedly attempting to deploy naval mines around the Strait of Hormuz.
“In addition to many other elements of the agreement, the Strait of Hormuz will be opened,” he said.
There were selloffs in heavyweight and mid-cap stocks such as BUA Cement, CAP, E-Tranzact International, International Breweries, Deap Capital Management and 20 others.
Mr Trump said in a post on the Truth Social platform that the strike, scheduled for Tuesday, was called off as “serious negotiations are now taking place”.
Major roads in Nairobi were blocked, leaving commuters stranded.
