diff --git a/stan/math/prim/prob/von_mises_lpdf.hpp b/stan/math/prim/prob/von_mises_lpdf.hpp
index f8e5e1aa303..7a759d9f43d 100644
--- a/stan/math/prim/prob/von_mises_lpdf.hpp
+++ b/stan/math/prim/prob/von_mises_lpdf.hpp
@@ -81,8 +81,8 @@ return_type_t<T_y, T_loc, T_scale> von_mises_lpdf(T_y const& y, T_loc const& mu,
   if (!is_constant_all<T_scale>::value) {
     edge<2>(ops_partials).partials_
         = cos_mu_minus_y
-          - modified_bessel_first_kind(1, kappa_val)
-                / modified_bessel_first_kind(0, kappa_val);
+          - exp(log_modified_bessel_first_kind(1, kappa_val)
+                - log_modified_bessel_first_kind(0, kappa_val));
   }
 
   return ops_partials.build(logp);