diff --git a/r/src/array_to_vector.cpp b/r/src/array_to_vector.cpp
index d92eaaea0a2..27fe6d15070 100644
--- a/r/src/array_to_vector.cpp
+++ b/r/src/array_to_vector.cpp
@@ -721,6 +721,10 @@ std::shared_ptr<Converter> Converter::Make(const std::shared_ptr<DataType>& type
       return std::make_shared<arrow::r::Converter_Promotion<REALSXP, arrow::UInt32Type>>(
           std::move(arrays));
 
+    case Type::UINT64:
+      return std::make_shared<arrow::r::Converter_Promotion<REALSXP, arrow::UInt64Type>>(
+          std::move(arrays));
+
     case Type::HALF_FLOAT:
       return std::make_shared<
           arrow::r::Converter_Promotion<REALSXP, arrow::HalfFloatType>>(
diff --git a/r/tests/testthat/test-Array.R b/r/tests/testthat/test-Array.R
index b105d2b158d..8749cd26426 100644
--- a/r/tests/testthat/test-Array.R
+++ b/r/tests/testthat/test-Array.R
@@ -385,6 +385,14 @@ test_that("Array<int8>$as_vector() converts to integer (ARROW-3794)", {
   expect_equal(a$as_vector(), 0:255)
 })
 
+test_that("Arrays of uint{32,64} convert to numeric", {
+  u32 <- Array$create(1L)$cast(uint32())
+  expect_identical(as.vector(u32), 1)
+
+  u64 <- Array$create(1L)$cast(uint64())
+  expect_identical(as.vector(u64), 1)
+})
+
 test_that("Array$create() recognise arrow::Array (ARROW-3815)", {
   a <- Array$create(1:10)
   expect_equal(a, Array$create(a))
diff --git a/r/vignettes/arrow.Rmd b/r/vignettes/arrow.Rmd
index c9ae799bcf9..83e6b374034 100644
--- a/r/vignettes/arrow.Rmd
+++ b/r/vignettes/arrow.Rmd
@@ -129,7 +129,7 @@ In the tables, entries with a `-` are not currently implemented.
 | uint8             | integer                  |
 | uint16            | integer                  |
 | uint32            | double                   |
-| uint64            | -                        |
+| uint64            | double                   |
 | float16           | -                        |
 | float32           | double                   |
 | float64           | double                   |