The Croatia international played the whole of Tuesday's 0-0 Champions League quarter-final first leg draw at home to Real Madrid but has been rested for the trip to Galicia, Simeone told a news conference.
Atletico's Spain midfielder Mario Suarez is also sidelined.
"I spoke to the doctor and Mandzukic has ankle pain and Mario some discomfort," Simeone said.
"Hopefully, we will have both of them back quickly so we can have a full squad available again."
Simeone did not say whether Mandzukic will be fit for Wednesday's Champions League return leg against Real, while Suarez suspended for the clash at the Bernabeu.
Fernando Torres will probably come into the team to replace Mandzukic against Deportivo, with Tiago filling in for Suarez in a defensive central midfield role.
Atletico are third in La Liga with seven games left, seven points behind second-placed Real, who host Malaga on Saturday. Leaders Barca are two points ahead of Real before they entertain Valencia, also on Saturday.
(Reporting by Iain Rogers, editing by Ed Osmond)
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