diff --git a/NEWS.md b/NEWS.md
index 6ff0c232da3fa..012e6747ec3a5 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -12,6 +12,8 @@ New language features
     `findall`, `findfirst`, `argmin`/`argmax` and `findmin`/`findmax` to work with these
     objects, returning the index of matching non-missing elements in the parent ([#31008]).
 
+  * `inv(::Missing)` has now been added and returns `missing` ([#31408]).
+
 Multi-threading changes
 -----------------------
 
diff --git a/base/missing.jl b/base/missing.jl
index 670a60d987ef7..e8db30d7c2f43 100644
--- a/base/missing.jl
+++ b/base/missing.jl
@@ -79,7 +79,7 @@ for f in (:(!), :(~), :(+), :(-), :(zero), :(one), :(oneunit),
           :(isinteger), :(isreal), :(isnan),
           :(iszero), :(transpose), :(adjoint), :(float), :(conj),
           :(abs), :(abs2), :(iseven), :(ispow2),
-          :(real), :(imag), :(sign))
+          :(real), :(imag), :(sign), :(inv))
     @eval ($f)(::Missing) = missing
 end
 for f in (:(Base.zero), :(Base.one), :(Base.oneunit))
diff --git a/base/number.jl b/base/number.jl
index 4a4b001b2a79f..7ec3f7425daf0 100644
--- a/base/number.jl
+++ b/base/number.jl
@@ -216,6 +216,9 @@ julia> inv(1 + 2im) * (1 + 2im)
 julia> inv(2//3)
 3//2
 ```
+
+!!! compat "Julia 1.2"
+    `inv(::Missing)` requires at least Julia 1.2.
 """
 inv(x::Number) = one(x)/x
 
diff --git a/test/missing.jl b/test/missing.jl
index d626c4222bd83..971f3a5d114aa 100644
--- a/test/missing.jl
+++ b/test/missing.jl
@@ -156,7 +156,7 @@ Base.one(::Type{Unit}) = 1
                             identity, zero, one, oneunit,
                             iseven, isodd, ispow2,
                             isfinite, isinf, isnan, iszero,
-                            isinteger, isreal, transpose, adjoint, float]
+                            isinteger, isreal, transpose, adjoint, float, inv]
 
     # All elementary functions return missing when evaluating missing
     for f in elementary_functions