diff --git a/src/python.cpp b/src/python.cpp
index 50dea48b..2693fbbf 100644
--- a/src/python.cpp
+++ b/src/python.cpp
@@ -367,8 +367,8 @@ bool has_null_bytes(PyObject* str) {
 }
 
 // helpers to narrow python array type to something convertable from R,
-// guaranteed to return NPY_BOOL, NPY_LONG, NPY_DOUBLE, or NPY_CDOUBLE
-// (throws an exception if it's unable to return one of these types)
+// guaranteed to return NPY_BOOL, NPY_LONG, NPY_DOUBLE, NPY_CDOUBLE,
+// or -1 if it's unable to return one of these types.
 int narrow_array_typenum(int typenum) {
 
   switch(typenum) {
@@ -412,7 +412,7 @@ int narrow_array_typenum(int typenum) {
 
     // unsupported
   default:
-    stop("Conversion from numpy array type %d is not supported", typenum);
+    typenum = -1;
     break;
   }
 
@@ -1432,6 +1432,10 @@ SEXP py_to_r_cpp(PyObject* x, bool convert, bool simple) {
     // determine the target type of the array
     int og_typenum = PyArray_TYPE(array);
     int typenum = narrow_array_typenum(og_typenum);
+    if (typenum == -1) {
+      simple = false;
+      goto cant_convert;
+    }
 
     if(og_typenum == NPY_DATETIME) {
       PyObjectPtr dtype_str(as_python_str("datetime64[ns]"));
@@ -1581,6 +1585,10 @@ SEXP py_to_r_cpp(PyObject* x, bool convert, bool simple) {
     PyArray_DescrPtr descrPtr(PyArray_DescrFromScalar(x));
     int og_typenum = descrPtr.get()->type_num;
     int typenum = narrow_array_typenum(og_typenum);
+    if (typenum == -1) {
+      simple = false;
+      goto cant_convert;
+    }
 
     PyObjectPtr x_;
     if(og_typenum == NPY_DATETIME) {
@@ -1675,6 +1683,7 @@ SEXP py_to_r_cpp(PyObject* x, bool convert, bool simple) {
 
   } // end convert == true && simple == true
 
+  cant_convert:
   Py_IncRef(x);
   return PyObjectRef(x, convert, simple);
 
diff --git a/tests/testthat/test-python-numpy.R b/tests/testthat/test-python-numpy.R
index 75056f05..41a11224 100644
--- a/tests/testthat/test-python-numpy.R
+++ b/tests/testthat/test-python-numpy.R
@@ -145,3 +145,43 @@ test_that("numpy string arrays are correctly handled", {
                                "17", "18"), byrow = TRUE, ncol = 2))
 
   })
+
+
+test_that("numpy non-simple arrays work", {
+  # https://github.com/rstudio/reticulate/issues/1613
+  py_run_string("import numpy as np", convert = FALSE)
+  py_run_string(
+    "array = np.array([(1.0, 2), (3.0, 4)], dtype=[('x', float), ('y', int)])",
+    convert = FALSE
+  )
+  result <- py_run_string("rec_array = array.view(np.recarray)", convert = FALSE)
+
+  # Test that attempting to convert a non-simple array fails gracefully,
+  # returns a PyObjectRef.
+  rec_array <- py_to_r(result$rec_array)
+  expect_equal(class(rec_array),
+               c("numpy.recarray", "numpy.ndarray", "python.builtin.object"))
+
+  # Test that a registered S3 method for the non-simple numpy array will be
+  # called. (Note, some packages, like {zellkonverter}, will register this
+  # directly for numpy.ndarray)
+  registerS3method("py_to_r", "numpy.recarray", function(x) {
+    tryCatch({
+      pandas <- import("pandas", convert = FALSE)
+      x <- pandas$DataFrame(x)$to_numpy()
+      x <- py_to_r(x)
+      return(x)
+    }, error = identity)
+    NextMethod()
+  })
+
+  on.exit({
+    rm(list = "py_to_r.numpy.recarray",
+       envir = environment(py_to_r)$.__S3MethodsTable__.)
+  })
+
+  arr <- py_to_r(result$rec_array)
+  expect_identical(arr, rbind(c(1, 2),
+                              c(3, 4)))
+
+})