diff --git a/ci/PKGBUILD b/ci/PKGBUILD
index 7eb0598b5dd..917335cdeae 100644
--- a/ci/PKGBUILD
+++ b/ci/PKGBUILD
@@ -28,7 +28,9 @@ depends=("${MINGW_PACKAGE_PREFIX}-boost"
          "${MINGW_PACKAGE_PREFIX}-double-conversion"
          "${MINGW_PACKAGE_PREFIX}-thrift"
          "${MINGW_PACKAGE_PREFIX}-snappy"
-         "${MINGW_PACKAGE_PREFIX}-zlib")
+         "${MINGW_PACKAGE_PREFIX}-zlib"
+         "${MINGW_PACKAGE_PREFIX}-lz4"         
+         "${MINGW_PACKAGE_PREFIX}-zstd")
 makedepends=("${MINGW_PACKAGE_PREFIX}-cmake"
              "${MINGW_PACKAGE_PREFIX}-gcc")
 options=("staticlibs" "strip" "!buildflags")
@@ -85,6 +87,8 @@ build() {
     -DARROW_JEMALLOC=OFF \
     -DARROW_WITH_ZLIB=ON \
     -DARROW_WITH_SNAPPY=ON \
+    -DARROW_WITH_LZ4=ON \
+    -DARROW_WITH_ZSTD=ON \
     -DARROW_USE_GLOG=OFF \
     -DARROW_BUILD_UTILITIES=OFF \
     -Ddouble-conversion_ROOT="${MINGW_PREFIX}" \
diff --git a/ci/windows-pkg-arrow-for-r.sh b/ci/windows-pkg-arrow-for-r.sh
index 23a518bad83..ae9a52b51b0 100644
--- a/ci/windows-pkg-arrow-for-r.sh
+++ b/ci/windows-pkg-arrow-for-r.sh
@@ -64,6 +64,12 @@ wget https://dl.bintray.com/rtools/mingw32/mingw-w64-i686-double-conversion-3.1.
 wget https://dl.bintray.com/rtools/mingw64/mingw-w64-x86_64-openssl-1.1.1.a-1-any.pkg.tar.xz
 wget https://dl.bintray.com/rtools/mingw32/mingw-w64-i686-openssl-1.1.1.a-1-any.pkg.tar.xz
 
+wget https://dl.bintray.com/rtools/mingw64/mingw-w64-x86_64-zstd-1.4.3-1-any.pkg.tar.xz
+wget https://dl.bintray.com/rtools/mingw32/mingw-w64-i686-zstd-1.4.3-1-any.pkg.tar.xz
+
+wget https://dl.bintray.com/rtools/mingw64/mingw-w64-x86_64-lz4-1.8.2-1-any.pkg.tar.xz
+wget https://dl.bintray.com/rtools/mingw32/mingw-w64-i686-lz4-1.8.2-1-any.pkg.tar.xz
+
 # These are the other Rtools 4.0 packages, for future reference
 # wget https://dl.bintray.com/rtools/mingw32/mingw-w64-i686-boost-1.67.0-9002-any.pkg.tar.xz
 # wget https://dl.bintray.com/rtools/mingw64/mingw-w64-x86_64-boost-1.67.0-9002-any.pkg.tar.xz
diff --git a/r/configure.win b/r/configure.win
index f1c93ac5862..74003b3bec7 100644
--- a/r/configure.win
+++ b/r/configure.win
@@ -41,7 +41,7 @@ RWINLIB="../windows/$(ls windows/ | grep ^arrow-)"
 OPENSSL_LIBS="-lcrypto -lcrypt32"
 
 PKG_CFLAGS="-I${RWINLIB}/include -DARROW_STATIC -DPARQUET_STATIC -DARROW_DS_STATIC -DARROW_R_WITH_ARROW"
-PKG_LIBS="-L${RWINLIB}/lib"'$(subst gcc,,$(COMPILED_BY))$(R_ARCH) '"-L${RWINLIB}/lib"'$(R_ARCH) '"-lparquet -larrow_dataset -larrow -lthrift -lsnappy -lboost_regex-mt-s -lboost_system-mt-s -lz ${OPENSSL_LIBS} -lws2_32"
+PKG_LIBS="-L${RWINLIB}/lib"'$(subst gcc,,$(COMPILED_BY))$(R_ARCH) '"-L${RWINLIB}/lib"'$(R_ARCH) '"-lparquet -larrow_dataset -larrow -lthrift -lsnappy -lboost_regex-mt-s -lboost_system-mt-s -lz -lzstd -llz4 ${OPENSSL_LIBS} -lws2_32"
 
 echo "*** Writing Makevars.win"
 sed -e "s|@cflags@|$PKG_CFLAGS|" -e "s|@libs@|$PKG_LIBS|" src/Makevars.in > src/Makevars.win
diff --git a/r/tests/testthat/test-compressed.R b/r/tests/testthat/test-compressed.R
index 93d4e334d0b..dcb5c52b935 100644
--- a/r/tests/testthat/test-compressed.R
+++ b/r/tests/testthat/test-compressed.R
@@ -25,6 +25,13 @@ test_that("codec_is_available", {
   expect_true(codec_is_available("GZIP"))
 })
 
+if (identical(Sys.getenv("APPVEYOR"), "True")) {
+  test_that("Compression codecs are included in the Windows build", {
+    expect_true(codec_is_available("lz4"))
+    expect_true(codec_is_available("zstd"))
+  })
+}
+
 test_that("Codec attributes", {
   skip_if_not_available("gzip")
   cod <- Codec$create("gzip")