diff --git a/stdlib/Dates/src/arithmetic.jl b/stdlib/Dates/src/arithmetic.jl
index be712905188f1..6537f4e1caa82 100644
--- a/stdlib/Dates/src/arithmetic.jl
+++ b/stdlib/Dates/src/arithmetic.jl
@@ -84,6 +84,12 @@ end
 (-)(x::Time, y::TimePeriod) = return Time(Nanosecond(value(x) - tons(y)))
 (+)(y::Period, x::TimeType) = x + y
 
+# Missing support
+(+)(x::AbstractTime, y::Missing) = missing
+(+)(x::Missing, y::AbstractTime) = missing
+(-)(x::AbstractTime, y::Missing) = missing
+(-)(x::Missing, y::AbstractTime) = missing
+
 # AbstractArray{TimeType}, AbstractArray{TimeType}
 (-)(x::OrdinalRange{T}, y::OrdinalRange{T}) where {T<:TimeType} = Vector(x) - Vector(y)
 (-)(x::AbstractRange{T}, y::AbstractRange{T}) where {T<:TimeType} = Vector(x) - Vector(y)
diff --git a/stdlib/Dates/test/arithmetic.jl b/stdlib/Dates/test/arithmetic.jl
index fe49b1127f9bf..a1a6884d4b0c3 100644
--- a/stdlib/Dates/test/arithmetic.jl
+++ b/stdlib/Dates/test/arithmetic.jl
@@ -499,4 +499,13 @@ end
     end
 end
 
+@testset "Missing arithmetic" begin
+    for t ∈ [Date, Time, Day, Month, Week, Year, Hour, Microsecond, Millisecond, Minute, Nanosecond, Second]
+        @test ismissing(t(1) + missing)
+        @test ismissing(missing + t(1))
+        @test ismissing(t(1) - missing)
+        @test ismissing(missing - t(1))
+    end
+end
+
 end