The incident occurred last night, with the traditional flat-bottomed boat overturning off Bettenty, an island area just north of The Gambia, with 72 on board.
All except two of those on board were women, said Commander Umar Kane, a senior firefighting official.
"Unfortunately, we have 20 bodies and one person missing," Kane told AFP, saying another 51 people had been rescued.
He said there were only two men on board.
The boat capsized as the women were on their way to look for seafood, he said. The incident occurred in a coastal area well known for its delicacies like oysters, where tourists flock in large numbers.
It was not immediately clear what caused the accident, with divers called in to help the search, Kane said.
L'Observateur daily said the boat had capsized in high winds, while other newspapers said it had foundered because it was overloaded.
Several papers recalled the Joola tragedy of 2002 when a ferry sunk during a storm, killing more than 1,800 people in what was one of the world's worst-ever maritime disasters.
In that incident, the ferry was licensed to hold just 580 people, including crew, but investigators found it was carrying well over 2,000 when it went down while passing the Gambian coast.
The Bettenty sinking came 12 days after a deadly fire ripped through a Muslim retreat in southeastern Senegal killing around 30 people.
Police are still investigating the cause of the blaze which hit a site visited every year by hundreds and sometimes thousands of pilgrims from the country's powerful Tijaniyya Muslim brotherhood.
Initial reports suggested it may have been caused by a gas canister which exploded while pilgrims were making tea in a straw shelter, with police arresting four people.
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