diff --git a/stan/math/prim/meta/holder.hpp b/stan/math/prim/meta/holder.hpp
index 130ecf6b22d..8ee9d6984ff 100644
--- a/stan/math/prim/meta/holder.hpp
+++ b/stan/math/prim/meta/holder.hpp
@@ -479,9 +479,13 @@ inline auto make_holder_impl(F&& func, std::index_sequence<Is...>,
 template <typename F, typename... Args,
           require_not_plain_type_t<std::invoke_result_t<F, Args&&...>>*>
 inline auto make_holder(F&& func, Args&&... args) {
-  return internal::make_holder_impl(std::forward<F>(func),
-                                    std::make_index_sequence<sizeof...(Args)>(),
-                                    std::forward<Args>(args)...);
+  if constexpr (is_var_matrix_v<std::invoke_result_t<F, Args&&...>>) {
+    return std::forward<F>(func)(std::forward<Args>(args)...);
+  } else {
+    return internal::make_holder_impl(
+        std::forward<F>(func), std::make_index_sequence<sizeof...(Args)>(),
+        std::forward<Args>(args)...);
+  }
 }
 
 /**
diff --git a/stan/math/prim/meta/is_var_matrix.hpp b/stan/math/prim/meta/is_var_matrix.hpp
index dbdafb67674..4cff3d132fd 100644
--- a/stan/math/prim/meta/is_var_matrix.hpp
+++ b/stan/math/prim/meta/is_var_matrix.hpp
@@ -19,6 +19,8 @@ struct is_var_matrix
     : bool_constant<
           math::conjunction<is_var<T>, is_eigen<value_type_t<T>>>::value> {};
 
+template <typename T>
+inline constexpr bool is_var_matrix_v = is_var_matrix<std::decay_t<T>>::value;
 /*! \ingroup require_eigens_types */
 /*! \defgroup var_matrix_types var_matrix  */
 /*! \addtogroup var_matrix_types */
diff --git a/test/unit/math/rev/fun/transpose_test.cpp b/test/unit/math/rev/fun/transpose_test.cpp
new file mode 100644
index 00000000000..8c72b89410d
--- /dev/null
+++ b/test/unit/math/rev/fun/transpose_test.cpp
@@ -0,0 +1,27 @@
+#include <stan/math/rev.hpp>
+#include <test/unit/math/rev/util.hpp>
+#include <gtest/gtest.h>
+#include <test/unit/math/rev/fun/util.hpp>
+
+// Reproduces a compile error: calling `transpose` on a `var_value` that holds
+// a non-plain Eigen expression (e.g. a row/block of a `var_value` matrix). The
+// resulting `var_value<Eigen::Transpose<...>>` is not a plain type, so
+// `make_holder` tries to wrap the `var_value` in an Eigen `Holder` expression,
+// which fails because `var_value` has no `StorageKind`.
+TEST_F(AgradRev, RevMatrix_transpose_var_block) {
+  using stan::math::transpose;
+  using stan::math::var_value;
+
+  Eigen::MatrixXd m(2, 3);
+  m << 1, 2, 3, 4, 5, 6;
+  var_value<Eigen::MatrixXd> m_vv(m);
+
+  // m_vv.row(0) is a var_value<Eigen::Block<Eigen::Map<...>>>
+  auto rt = transpose(m_vv.row(0));
+
+  EXPECT_EQ(3, rt.rows());
+  EXPECT_EQ(1, rt.cols());
+  EXPECT_FLOAT_EQ(1, rt.val()(0));
+  EXPECT_FLOAT_EQ(2, rt.val()(1));
+  EXPECT_FLOAT_EQ(3, rt.val()(2));
+}