If a product is made entirely in a foreign country by a process that has been patented in the United States, would that constitute patent infringement?

Possibly. 

35 U.S.C. 271(g) states, in relevant part:

"Whoever without authority imports into the United States or offers to sell, sells, or uses within the United States a product which is made by a process patented in the United States shall be liable as an infringer, if the importation, offer to sell, sale, or use of the product occurs during the term of such process patent. In an action for infringement of a process patent, no remedy may be granted for infringement on account of the noncommercial use or retail sale of a product unless there is no adequate remedy under this title for infringement on account of the importation or other use, offer to sell, or sale of that product. A product which is made by a patented process will, for purposes of this title, not be considered to be so made after--
(1) it is materially changed by subsequent processes; or
(2) it becomes a trivial and nonessential component of another product."