diff --git a/dev/tasks/linux-packages/apache-arrow/apt/debian-forky/Dockerfile b/dev/tasks/linux-packages/apache-arrow/apt/debian-forky/Dockerfile
index 0f679f0388a6..0302516d7f75 100644
--- a/dev/tasks/linux-packages/apache-arrow/apt/debian-forky/Dockerfile
+++ b/dev/tasks/linux-packages/apache-arrow/apt/debian-forky/Dockerfile
@@ -88,3 +88,8 @@ RUN \
     apt install -y -V ${quiet} nvidia-cuda-toolkit; \
   fi && \
   apt clean
+
+# nvidia-cuda-toolkit was removed from Debian forky amd64, so disable the
+# CUDA packages via the pkg.apache-arrow.nocuda build profile.See GH-50090.
+# Once nvidia-cuda-toolkit is re-added to Debian forky, this can be removed.
+ENV DEB_BUILD_PROFILES=pkg.apache-arrow.nocuda
diff --git a/dev/tasks/linux-packages/apache-arrow/debian/control.in b/dev/tasks/linux-packages/apache-arrow/debian/control.in
index 0a82fb04ebcb..5434a21252d8 100644
--- a/dev/tasks/linux-packages/apache-arrow/debian/control.in
+++ b/dev/tasks/linux-packages/apache-arrow/debian/control.in
@@ -30,7 +30,11 @@ Build-Depends:
   meson,
   ninja-build,
   nlohmann-json-dev | nlohmann-json3-dev,
-  nvidia-cuda-toolkit [!arm64],
+# nvidia-cuda-toolkit may be unavailable (e.g. removed from Debian forky).
+# The pkg.apache-arrow.nocuda build profile (set via DEB_BUILD_PROFILES, e.g.
+# in the debian-forky Dockerfile) skips this build dependency and the CUDA
+# packages below.
+  nvidia-cuda-toolkit [!arm64] <!pkg.apache-arrow.nocuda>,
   pkg-config,
   protobuf-compiler,
   protobuf-compiler-grpc,
@@ -82,6 +86,7 @@ Description: Apache Arrow is a data processing library for analysis
 Package: libarrow-cuda2500
 Section: libs
 Architecture: @CUDA_ARCHITECTURE@
+Build-Profiles: <!pkg.apache-arrow.nocuda>
 Multi-Arch: same
 Pre-Depends: ${misc:Pre-Depends}
 Depends:
@@ -190,6 +195,7 @@ Description: Apache Arrow is a data processing library for analysis
 Package: libarrow-cuda-dev
 Section: libdevel
 Architecture: @CUDA_ARCHITECTURE@
+Build-Profiles: <!pkg.apache-arrow.nocuda>
 Multi-Arch: same
 Depends:
   ${misc:Depends},
@@ -369,6 +375,7 @@ Description: Apache Arrow is a data processing library for analysis
 Package: libarrow-cuda-glib2500
 Section: libs
 Architecture: @CUDA_ARCHITECTURE@
+Build-Profiles: <!pkg.apache-arrow.nocuda>
 Multi-Arch: same
 Pre-Depends: ${misc:Pre-Depends}
 Depends:
@@ -383,6 +390,7 @@ Description: Apache Arrow is a data processing library for analysis
 Package: libarrow-cuda-glib-doc
 Section: doc
 Architecture: @CUDA_ARCHITECTURE@
+Build-Profiles: <!pkg.apache-arrow.nocuda>
 Multi-Arch: foreign
 Depends:
   ${misc:Depends}
@@ -394,6 +402,7 @@ Description: Apache Arrow is a data processing library for analysis
 Package: gir1.2-arrow-cuda-25.0
 Section: introspection
 Architecture: @CUDA_ARCHITECTURE@
+Build-Profiles: <!pkg.apache-arrow.nocuda>
 Multi-Arch: same
 Depends:
   ${gir:Depends},
@@ -407,6 +416,7 @@ Description: Apache Arrow is a data processing library for analysis
 Package: libarrow-cuda-glib-dev
 Section: libdevel
 Architecture: @CUDA_ARCHITECTURE@
+Build-Profiles: <!pkg.apache-arrow.nocuda>
 Multi-Arch: same
 Depends:
   ${misc:Depends},