The freighter sank after the collision on Wednesday night, about 11km (7 miles) off the Indonesian island Batam, Singapore officials said.
It was carrying 560 tonnes of fuel but there are no reports of an oil spill.
The Singapore Strait is one of the busiest shipping lanes in the world, although major accidents are rare.
Officials said the tanker Stolt Commitment, registered in the Cayman Islands, collided with freighter Thorco Cloud, which had the Antigua and Barbuda flag, around 20:00 local time (1200 GMT). The tanker had only minor damage.
The missing are among the freighter's crew of 12 men. The rest were rescued and are currently being treated in a Singapore hospital.
Anti-pollution craft have been put on standby in case of an oil spill, said Singapore's marine and port authority.