The overhaul of the 110,000-bpd PSLA 9 CDU is scheduled to last two months. The work was expected to begin this month.
"The Baton Rouge Refinery has shut down some of its units and associated operations for planned maintenance beginning Feb 11," said Exxon spokeswoman Megan Manchester.
The sources said the 22,500 bpd coker was also shut on Monday for a planned overhaul.
Manchester did not identify the units shut at the Baton Rouge refinery.
CDUs do the primary refining of crude oil into feedstocks for all other production units, as well as producing unfinished motor fuels.
Cokers refine residual crude oil received from distillation units into motor fuel feedstocks.
(Reporting by Erwin Seba; Editing by Dan Grebler)