diff --git a/stan/math/fwd/fun/abs.hpp b/stan/math/fwd/fun/abs.hpp
index ffd21791ff0..1f50b149fd6 100644
--- a/stan/math/fwd/fun/abs.hpp
+++ b/stan/math/fwd/fun/abs.hpp
@@ -32,7 +32,7 @@ inline fvar<T> abs(const fvar<T>& x) {
  * @return absolute value of the argument
  */
 template <typename T>
-inline std::complex<fvar<T>> abs(const std::complex<fvar<T>>& z) {
+inline fvar<T> abs(const std::complex<fvar<T>>& z) {
   return internal::complex_abs(z);
 }
 
diff --git a/stan/math/rev/fun/abs.hpp b/stan/math/rev/fun/abs.hpp
index d77abd3e09e..9c9ad10dee4 100644
--- a/stan/math/rev/fun/abs.hpp
+++ b/stan/math/rev/fun/abs.hpp
@@ -44,9 +44,7 @@ inline var abs(const var& a) { return fabs(a); }
  * @param[in] z argument
  * @return absolute value of the argument
  */
-inline std::complex<var> abs(const std::complex<var>& z) {
-  return internal::complex_abs(z);
-}
+inline var abs(const std::complex<var>& z) { return internal::complex_abs(z); }
 
 }  // namespace math
 }  // namespace stan
diff --git a/test/unit/math/mix/fun/abs_test.cpp b/test/unit/math/mix/fun/abs_test.cpp
index 11f5da342b2..47b59f23bc7 100644
--- a/test/unit/math/mix/fun/abs_test.cpp
+++ b/test/unit/math/mix/fun/abs_test.cpp
@@ -2,8 +2,9 @@
 #include <cmath>
 #include <complex>
 #include <vector>
+#include <type_traits>
 
-TEST(mixScalFun, abs) {
+TEST(mixFun, abs) {
   auto f = [](const auto& x) {
     using std::abs;
     return abs(x);
@@ -29,3 +30,12 @@ TEST(mixScalFun, abs) {
     }
   }
 }
+TEST(mixFun, absReturnType) {
+  // validate return types not overpromoted to complex by assignability
+  std::complex<stan::math::var> a = 3;
+  stan::math::var b = abs(a);
+
+  std::complex<stan::math::fvar<double>> c = 3;
+  stan::math::fvar<double> d = abs(c);
+  SUCCEED();
+}