A search effort was launched for the four Chinese members of crew and one Malaysian after the accident around the busy Singapore Strait, the city-state's Maritime and Port Authority (MPA) said.
Seven other Chinese sailors were rescued from the Dominican-registered dredger after it capsized following the collision in the early hours, and were taken to hospital.
The Indonesian-registered tanker sustained damage to its front section but is stable and none of its crew members were hurt, the port authority said.
There was no disruption to shipping in the Singapore Strait, it added.
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On August 21, the destroyer USS John S. McCain collided with a tanker near the Singapore Strait, tearing a gaping hole in the ship's hull, and flooding it with water.
Ten US sailors were found dead inside flooded compartments after the collision, the latest accident involving an American warship in Asian waters.
The waters around Singapore are some of the busiest in the world, with huge numbers of cargo vessels plying the trade routes between Asia and Europe.