diff --git a/r/R/feather.R b/r/R/feather.R
index 5aaf340c6db..f8f3cb39354 100644
--- a/r/R/feather.R
+++ b/r/R/feather.R
@@ -147,14 +147,17 @@ read_feather <- function(file, col_select = NULL, as_data_frame = TRUE, ...) {
     file <- make_readable_file(file)
     on.exit(file$close())
   }
-  reader <- FeatherReader$create(file, ...)
+  reader <- FeatherReader$create(file)
 
   col_select <- enquo(col_select)
   columns <- if (!quo_is_null(col_select)) {
     vars_select(names(reader), !!col_select)
   }
 
-  out <- reader$Read(columns)
+  out <- tryCatch(
+    reader$Read(columns),
+    error = function(e) { read_compressed_error(e) }
+  )
 
   if (isTRUE(as_data_frame)) {
     out <- as.data.frame(out)
diff --git a/r/R/parquet.R b/r/R/parquet.R
index 45751b16170..689324113c2 100644
--- a/r/R/parquet.R
+++ b/r/R/parquet.R
@@ -52,10 +52,16 @@ read_parquet <- function(file,
     schema <- reader$GetSchema()
     names <- names(schema)
     indices <- match(vars_select(names, !!col_select), names) - 1L
-    tab <- reader$ReadTable(indices)
+    tab <- tryCatch(
+      reader$ReadTable(indices),
+      error = function(e) { read_compressed_error(e) }
+    )
   } else {
     # read all columns
-    tab <- reader$ReadTable()
+    tab <- tryCatch(
+      reader$ReadTable(),
+      error = function(e) { read_compressed_error(e) }
+    )
   }
 
   if (as_data_frame) {
diff --git a/r/R/util.R b/r/R/util.R
index 3362c0f4fda..97932cbaf0a 100644
--- a/r/R/util.R
+++ b/r/R/util.R
@@ -45,3 +45,16 @@ is_list_of <- function(object, class) {
 }
 
 empty_named_list <- function() structure(list(), .Names = character(0))
+
+read_compressed_error <- function(e) {
+  e <- as.character(e)
+  compression <- sub(".*Support for codec '(.*)'.*", "\\1", e)
+  msg <- c(
+    sprintf("Unsupported compressed format %s", compression),
+    "\nTry setting the environment variable LIBARROW_MINIMAL=false and reinstalling",
+    "\nfor a more complete installation ",
+    sprintf("(including %s) or setting", compression),
+    sprintf("\nARROW_WITH_%s=ON and reinstalling to enable support for this codec.", toupper(compression))
+    )
+  stop(msg, call. = FALSE)
+}
diff --git a/r/tests/testthat/test-feather.R b/r/tests/testthat/test-feather.R
index 52325c7f410..b0a9c6ff18e 100644
--- a/r/tests/testthat/test-feather.R
+++ b/r/tests/testthat/test-feather.R
@@ -196,3 +196,20 @@ test_that("Character vectors > 2GB can write to feather", {
 })
 
 unlink(feather_file)
+
+# lz4 ----
+
+ft_file <- test_path("golden-files/data-arrow_2.0.0_lz4.feather")
+
+test_that("Error messages are shown when the compression algorithm lz4
+          is not found", {
+  if (codec_is_available("lz4")) {
+    d <- read_feather(ft_file)
+    expect_is(d, "data.frame")
+  } else {
+    expect_error(
+      read_feather(ft_file),
+      "Unsupported compressed format"
+    )
+  }
+})
diff --git a/r/tests/testthat/test-parquet.R b/r/tests/testthat/test-parquet.R
index 4ac356f004d..89310d8af22 100644
--- a/r/tests/testthat/test-parquet.R
+++ b/r/tests/testthat/test-parquet.R
@@ -234,3 +234,11 @@ test_that("ParquetFileReader $ReadRowGroup(s) methods", {
   expect_true(reader$ReadRowGroups(c(0, 1), 0) == Table$create(x = 1:20))
   expect_error(reader$ReadRowGroups(c(0, 1), 1))
 })
+
+test_that("Error messages are shown when the compression algorithm lz4/snappy
+          is not found", {
+  if (codec_is_available("snappy")) {
+    d <- read_parquet(pq_file)
+    expect_is(d, "data.frame")
+  }
+})