BRUSSELS—The escalating trade war between the U.S. and Europe threatens a commercial relationship that is worth an estimated $9.5 trillion in two-way trade and investment, say American businesses caught in the crossfire.

The American Chamber of Commerce to the European Union, which represents U.S. companies that operate in Europe, said tariffs risk damaging far more than just sales of goods that are directly taxed. They could also harm trans-Atlantic investments, which are more than three times as valuable.