The 224-metre (735ft) El Faro, with 28 Americans and five Poles on board, was last heard from on Thursday and was reported to be taking on water.
The ship – which was travelling from Florida to Puerto Rico – was also believed to be listing at 15 degrees.
Joaquin brought heavy rains to the Bahamas, damaging a number of houses.
There have been no reports of casualties so far.
The now-weaker Category Four storm – with sustained winds of up to 210km/h (130mph) – is moving away from the island nation in the Atlantic.
US officials said they believed any threat to the East Coast was fading.
We’re going to go and try and save lives,” Coast Guard Cpt Mark Fedor said on Saturday, Associated Press reported.
“We’re going to push it to the operational limits as far as we can.”
Cpt Fedor added that waves of up to nine metres and heavy winds could have destroyed El Faro’s communications equipment.
The Coast Guard said it had already covered more than 850 sq miles (2,200 sq km) in the search for the vessel.
El Faro’s owner, Florida-based TOTE Services, said it was working together with the Coast Guard to try to re-establish contact with the ship.