diff --git a/src/deprecations.jl b/src/deprecations.jl
index 101790f9..2c21ea78 100644
--- a/src/deprecations.jl
+++ b/src/deprecations.jl
@@ -1,4 +1,8 @@
 # Removed with 0.16, indexing via non-integers
+getindex(itp::AbstractInterpolation{T,N}, i::Vararg{Number,N}) where {T,N} =
+    error("Indexing an AbstractInterpolation by non-integers is no longer supported in Interpolations.jl since v0.16. Use the function calling interface instead: `itp(i...)`.")
+getindex(itp::AbstractInterpolation{T,N}, i::Vararg{ExpandedIndexTypes,N}) where {T,N} =
+    error("Indexing an AbstractInterpolation by non-integers is no longer supported in Interpolations.jl since v0.16. Use the function calling interface instead: `itp(i...)`.")
 
 for T in (:Throw, :Flat, :Line, :Free, :Periodic, :Reflect, :InPlace, :InPlaceQ)
     @eval begin
diff --git a/test/issues/runtests.jl b/test/issues/runtests.jl
index 7c1ca52e..cb549a47 100644
--- a/test/issues/runtests.jl
+++ b/test/issues/runtests.jl
@@ -177,4 +177,10 @@ using Interpolations, Test, ForwardDiff
         t = -3.0:0.01:3.0
         @test itp_cdf.(t) isa Vector{Float64}
     end
+    @testset "issue 630" begin
+        itp = interpolate(ones(100,100), BSpline(Linear()));
+        # Indexing by non-integers should not result in a StackOverflow due to `Base.to_index(::AbstractInterpolation, x::Number) = x`
+        @test_throws "Indexing an AbstractInterpolation by non-integers is no longer supported" itp[2.2, 33.3]
+        @test_throws "Indexing an AbstractInterpolation by non-integers is no longer supported" itp[2.2, 2.0:5.0]
+    end
 end