diff --git a/NEWS.md b/NEWS.md
index b5ad2ff69..a454a7793 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -26,6 +26,9 @@
 * Correctly return `Bool[]` in the `nonunique` function applied to a data frame
   with a pulled column that has zero levels in the pool
   ([#3393](https://github.com/JuliaData/DataFrames.jl/pull/3393))
+* Correctly index `eachrow` and `eachcol` with `CartesianIndex`
+  ([#3413](https://github.com/JuliaData/DataFrames.jl/issues/3413))
+
 
 # DataFrames.jl v1.6.1 Release Notes
 
diff --git a/src/abstractdataframe/iteration.jl b/src/abstractdataframe/iteration.jl
index c81228fb1..6f6abc620 100644
--- a/src/abstractdataframe/iteration.jl
+++ b/src/abstractdataframe/iteration.jl
@@ -81,6 +81,7 @@ Base.IndexStyle(::Type{<:DataFrameRows}) = Base.IndexLinear()
 Base.size(itr::DataFrameRows) = (size(parent(itr), 1), )
 
 Base.@propagate_inbounds Base.getindex(itr::DataFrameRows, i::Int) = parent(itr)[i, :]
+Base.@propagate_inbounds Base.getindex(itr::DataFrameRows, i::CartesianIndex{1}) = itr[i[1]]
 Base.@propagate_inbounds Base.getindex(itr::DataFrameRows, idx) =
     eachrow(@view parent(itr)[idx isa AbstractVector && !(eltype(idx) <: Bool) ? copy(idx) : idx, :])
 
@@ -263,6 +264,8 @@ Base.iterate(itr::DataFrameColumns, i::Integer=1) =
     i <= length(itr) ? (itr[i], i + 1) : nothing
 Base.@propagate_inbounds Base.getindex(itr::DataFrameColumns, idx::ColumnIndex) =
     parent(itr)[!, idx]
+Base.@propagate_inbounds Base.getindex(itr::DataFrameColumns, idx::CartesianIndex{1}) =
+    itr[idx[1]]
 Base.@propagate_inbounds Base.getindex(itr::DataFrameColumns, idx::MultiColumnIndex) =
     eachcol(parent(itr)[!, idx])
 Base.:(==)(itr1::DataFrameColumns, itr2::DataFrameColumns) =
diff --git a/test/iteration.jl b/test/iteration.jl
index 4c1b9d0d1..249677a02 100644
--- a/test/iteration.jl
+++ b/test/iteration.jl
@@ -15,6 +15,8 @@ using Test, DataFrames
     @test sprint(summary, eachrow(df)) == "2-element DataFrameRows"
     @test Base.IndexStyle(eachrow(df)) == IndexLinear()
     @test eachrow(df)[1] == DataFrameRow(df, 1, :)
+    @test eachrow(df)[CartesianIndex(1)] == DataFrameRow(df, 1, :)
+    @test_throws MethodError eachrow(df)[CartesianIndex(1, 1)]
     @test collect(eachrow(df)) isa Vector{<:DataFrameRow}
     @test eltype(eachrow(df)) <: DataFrameRow
     for row in eachrow(df)
@@ -35,6 +37,8 @@ using Test, DataFrames
     @test_throws ArgumentError size(eachcol(df), 2)
     @test_throws ArgumentError size(eachcol(df), 0)
     @test eachcol(df)[1] == df[:, 1]
+    @test eachcol(df)[CartesianIndex(1)] == df[:, 1]
+    @test_throws MethodError eachcol(df)[CartesianIndex(1, 1)]
     @test eachcol(df)[:A] === df[!, :A]
     @test eachcol(df)[All()] == eachcol(df)
     @test eachcol(df)[Cols(:)] == eachcol(df)