The following material was provided by Al Rice, curator of the Fiske Museum of Musical Instruments.
The Fifty-first congress, session I, chapter 1244 (October 1, 1890) is entitled "An act to reduce the revenue and equalize duties on imports, and for other purposes." I believe that this is the first time a tariff act with this provision was enacted.
Section 6 is the relevant section which states "That on and after the first day of March, eighteen hundred and ninety-one, all articles of foreign manufacture, such as are usually or ordinarily marked, stamped, branded, or labeled, and all packages containing such or other imported articles, shall, respectively, be plainly marked, stamped, branded, or labeled in legible English words, so as to indicate the country of their origin; and unless so marked, stamped, branded, or labeled they shall not be admitted to entry." This is repeated with slight changes in 1894 and 1897.
The section is carried in later versions passed by later congresses with some interesting additions. The sixty-first congress of 1909 (Chapter 6, section 6) states "That all articles of foreign manufacture or production, which are capable of being marked, stamped, branded, or labeled, without injury, shall be marked, stamped, branded, or labeled in legible English words, in a conspicuous place that shall not be covered or obscured by an subsequent attachments or arrangements, so as to indicate the country of origin. Said marking, stamping, branding, or labeling shall be as nearly indelible and permanent as the nature of the article will permit."
The same wording is continued in 1913 and 1922.