The US president reacts to new EU tariffs on imports of US jeans, motorbikes, bourbon, cranberries and other products.
His threat - which if carried out would represent a serious escalation of the burgeoning trade war - comes hours after new EU tariffs on goods imported from the US came into force.
In response to Mr Trump's tariffs on European steel and aluminium, the EU has imposed tariffs on imports of US cranberries, orange juice, sweetcorn, peanut butter, bourbon whiskey, cigarettes, cigars, cheroots (a type of thin cigar), cosmetics, motorbikes, boats, jeans, leather footwear, swimwear, underwear and steel products.
The US president tweeted: "Based on the Tariffs and Trade Barriers long placed on the U.S. and its great companies and workers by the European Union, if these Tariffs and Barriers are not soon broken down and removed, we will be placing a 20% Tariff on all of their cars coming into the U.S. Build them here!"
Just 20 minutes before the president's tweet, the EU's ambassador to the US, David O'Sullivan, tweeted "that the EU-US economic relationship is the most important in the world bar none".
President Trump is pushing ahead with his campaign pledge to protect American jobs and has described trading relationships with his neighbours and allies as unfair.
The US has imposed tariffs valued at £25bn on Chinese goods - as well as on imports from Canada and Mexico.
China, India, Mexico, Canada and Turkey are among those to so far hit back with their own tariffs on US imports.
European Commission President Jean-Claude Juncker said on Thursday the US's new stance on trade "goes against all logic and history".
A spokesman for Prime Minister Theresa May said she expects to discuss trade tariffs with the US president during his UK visit in July.
Global stock markets, which have largely ignored Mr Trump's complaints as "bluster" and a negotiating ploy, are getting more jittery as nations retaliate.