The fire at Mame Abdou Aziz Sy Dabakh Hospital was in the maternity department, President Macky Sall tweeted.
Initial reports suggest the fire was caused by a short circuit, according to Senegalese politicians.
Three babies were saved from the fire, said the city's mayor, Demba Diop Sy.

The fire spread very quickly and emergency services were still at the scene, Mr Sy told local media.
The hospital had been newly inaugurated, according to AFP, citing local media reports.