"Two members of the crew were rescued but two others are missing," police spokesman Paul-Heinz Meurisch said.
Melting snow and rains have swollen rivers in the western German region but it was not immediately known if that was a factor in the accident on Germany's longest river, which
was reported around 5:00 am (0400 GMT).
Helicopters equipped with infrared equipment took to the air to search for the missing crew, and traffic on the river, a major European transport artery, was suspended. The ship measures roughly 100 metres (yards) long and was completely turned over, with its keel above the waterline, but it was not immediately known if any acid had leaked into the river, Meurisch said.
The accident occurred near a celebrated rock outcropping known as "Lorelei," a nymph from German mythology that was said to attract mariners with enchanting songs.
The site sits above a particularly narrow point in the river where the current is very strong and many accidents have taken place in the past.