Does it prevent us from shipping to US clients? Or does it only
refrain us from manufacturing the product on US soil?
Yes it is accounted as infringement under 35 USC 271 which is quoted below for you ready reference.
35 U.S. Code § 271 - Infringement of patent
(a) Except as otherwise provided in this title, whoever without authority makes, uses, offers to sell, or sells any patented invention, within the United States or imports into the United States any patented invention during the term of the patent therefor, infringes the patent.
(b) Whoever actively induces infringement of a patent shall be liable as an infringer.
(c) Whoever offers to sell or sells within the United States or imports into the United States a component of a patented machine, manufacture, combination or composition, or a material or apparatus for use in practicing a patented process, constituting a material part of the invention, knowing the same to be especially made or especially adapted for use in an infringement of such patent, and not a staple article or commodity of commerce suitable for substantial noninfringing use, shall be liable as a contributory infringer.