Trains-to-turbines group Siemens employs more than 50,000 people in the United States, its single biggest market, where it makes 21 percent of its total revenue, while BMW's South Carolina plant is its largest factory anywhere in the world.
Mr Trump will meet Ms Merkel, Europe's longest-serving leader, for the first time on Tuesday in Washington. A German government spokesman confirmed at a press conference on Monday that the two leaders would also meet with German company representatives.
German chancellors have a long tradition of taking groups of business leaders along with them on trips to important countries. Those accompanying Ms Merkel will include the chief executive of ball-bearings maker Schaeffler.
Sources of tension between Berlin and the new US administration include an accusation by a senior Trump adviser that Germany profits unfairly from a weak euro, and Mr Trump's threat to impose 35 per cent tariffs on imported vehicles.
The United States is Germany's biggest trading partner, buying German goods and services worth 107 billion euros ($114 billion) last year while exporting just 58 billion euros' worth in return.
As part of a bid to bring jobs to America, Mr Trump has urged carmakers to build more cars in the United States and discouraged them from investing in Mexico, where German and other carmakers have big plants.
Mr Trump's order banning citizens of some majority-Muslim countries from entering the United States, and a threat to tear up the NAFTA free trade deal between the United States, Mexico and Canada, have also unnerved business leaders.
Siemens chief executive Joe Kaeser expressed concern last month about developments in the United States since Trump took office, saying: "The new American president has a style that's different from what we're accustomed to. It worries us, what we see."
BMW's Chief Executive Harald Krueger meanwhile said last week that introducing protectionist measures and tariffs would not be good for the United States.
The carmaker is expanding its plant in Spartanburg, South Carolina, to have a capacity of 450,000 vehicles, 70 per cent of which are for export.
It is also building a new plant in Mexico, where it plans to invest $2.2 billion by 2019. Mexico's lower labour costs and unique free trade position mean it now accounts for a fifth of all vehicle production in North America.
"America profits from free trade. We are supporters of free trade and not of protectionism," Mr Krueger told reporters at the Geneva auto show.