Using sources like the Kebra Nagast, it seems as if the Queen of Sheba and King Solomon had a child together. That child (Menelik) ended up taking the Ark back home years later, but then Sheba (Saba) was actually not in Ethiopia, but in the Arabian peninsula... so much murky waters, but what's the current view (if any)?
There is no historical evidence that the Ark of the Covenant is a real object, so it is probably not in Ethiopia.