The firm said in a statement its flights would continue to operate using alternative routes, adding the decision was in line with guidance issued by the US Federal Aviation Administration.
This follows announcements by other airlines including KLM and Qantas, to do the same, all citing safety fears.
BA’s flights will avoid the Strait of Hormuz – a vital trade route for oil transportation in the Gulf and fringes Iran’s southern border.
Earlier that day he tweeted: “Iran made a big mistake!”
Russia’s deputy foreign minister warned that recent clashes between Tehran and Washington was pushing the world to the “brink of war”.
Iran told the Swiss ambassador that the US will face consequences if they launch military action.
This comes after Iran shot down a US spy drone near the Strait of Hormuz, with both sides giving conflicting versions of what happened.
Iran claims it was a defensive move from inside its own territory, and said “our airspace is our red line”, but the US said the drone was operating above “international territory”.
Tehran now claims it gave a 10 minute warning before downing the drone, CNN reports.
Tensions between the nations have been boiling since the US imposed sanctions against Iran, crippling its ability to trade oil.
Last month, Trump promised “severe consequences” against the UK and other EU nations if they continue to trade with Iran.
A senior British admiral warned that the US “would need a million men” to wage war and obliterate the regime in Iran.