Barry is suffering from a hip problem while Monaghan has a knee complaint.
"The League Cup is a competition that Derry have a reputation of having great success in and I would like to continue that," said Derry manager Kenny Shiels.
"We will go in as full strength as we can be. We treat the competition with the utmost respect and want to win it."
The Candystripes go into the cup tie unbeaten in their last seven league outings but will have had a day less to prepare given that they drew with Longford Town on Saturday night.
"Sligo haven't won a game yet in the league but they have been getting progressively better and I like the way they play so we have to be careful with this one," emphasised the Derry boss.
"The league is the platform you use for building for the future but the knockout competitions are important for morale and a good cup run gives a boost to the supporters.
"We always look to the next game as the most important and we try to win every game. From Sligo's point of view, they will see this as a chance to gain some momentum."
Derry City will be missing injured duo Aaron Barry and Harry Monaghan for their EA Sports Cup second round tie against Sligo Rovers at the Brandywell.