The production of φ mesons in proton collisions with C, Cu, Ag, and Au targets has been studied via the φ → K + K − decay at an incident beam energy of 2.83 GeV using the ANKE detector system at COSY. For the first time, the momentum dependence of the nuclear transparency ratio, the in-medium φ width, and the differential cross section for φ -meson production at forward angles have been determined for these targets over the momentum range of 0.6-1.6 GeV /c. There are indications of a significant momentum dependence in the value of the extracted φ width, which corresponds to an effective φN absorption cross section in the range of 14-21 mb.