Speaking at the Scottish Parliament on Thursday, he said tariffs of 25% on goods including Scotch whisky, biscuits and woollen and cashmere products will have a direct impact on businesses.
US President Donald Trump has been a vocal proponent of imposing tariffs on foreign goods.
Mr McKee said: “Trade disputes may seem far removed from most people’s day-to-day lives, but the impact of these tariffs on Scottish businesses, and potential on people’s jobs, is immediate and real.
“Single malt Scotch whisky, cheese, butter, cashmere, and sweet biscuits including shortbread, are targeted by the tariffs.
“This is profoundly worrying for Scottish producers exporting, or planning to export, to the US.”
He added that the impact of the tariffs is being felt across Scotland - “from the villages of Speyside to the west coast island distilleries and the textile manufacturers of the Borders”.
He added: “These US tariffs have seen Scotland caught up in a trade dispute not of our making.
“They have a direct impact on Scottish businesses, but post-Brexit tariffs with the EU would multiply the scale of this impact on the Scottish economy.
“Our healthy current trade with the US shows that we do not need to leave the EU to trade successfully with the US.
“We can increase our exports to 25% of our GDP in the next 10 years, but Scotland’s voice must be heard and our interests represented in future trade deals.”
Scottish Conservative MSP Dean Lockhart said Scotch whisky and other vital sectors had become collateral damage in a much wider US-EU trade dispute.
He added: “The only reason Scotch whisky and other sectors are being hit with US tariffs is because we are still members of the EU.
“And because in this trade dispute, the EU has prioritised the interests of European aerospace, French champagne and other European sectors at the expense of Scotch whisky.
“The reality is that after Brexit, we will be free to negotiate our own free trade agreements with the rest of the world.”
Liberal Democrat MSP Mike Rumbles said: “Despite the current US president’s warm words about Brexit, his aggressive nationalism and protectionism tell a different story. His values are not the values that we share.”