Iraqi Yazidi Islamic State survivors and activists Nadia Murad and Lamiya Aji Bashar received the award during an emotional ceremony in Parliament on Tuesday.
After escaping sexual enslavement by Islamic State, they both became spokespeople for women affected by the terrorist group's campaign of sexual violence and for the persecuted Yazidi minority.
Speaking at a news conference after the ceremony, Schulz also called for IS operatives to "face justice" for "crimes against humanity" at the International Court in The Hague.
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The German MEP said he was "extremely moved" by the two women's acceptance speeches, adding, "They spoke of unspeakable crimes against humanity.
"It was noticeable that those MEPs who deny there is a refugee problem were absent from their seats during their speeches."
Schulz, who will return to German politics in the new year, also said, "This is my last news conference in Parliament and I am proud that it was with two such brave women."
He said, "There should be no impunity for those who carry out such atrocities. That has to be the message going out today."
His appeal for the international community to bring IS to justice was echoed by Murad who said, "It is important that those responsible are put in the dock."
Aji Bashar said, "Other groups may replace IS, so it is important that there is an international protection zone so that people like us can return to Syria in safety."
She narrated her ordeal at the hands of Islamic State and how she was seriously disfigured during her escape while her childhood friend and another girl died.
"I was sold four times by Daesh. Together with a friend of mine called Kathrin and a nine-year-old girl, all of us were raped," she said.
"The three of us did actually manage to escape but before we actually managed to arrive to safety, Kathrin accidentally walked over a landmine and it exploded and the last thing I heard was her death screams and it was the worst thing I have ever heard."
Aji Bashar told deputies, "I believe I can be a voice to the victims. And the Sakharov Prize gives me great strength and this is why I have taken the decision to become a voice for the voiceless."
She added, "More than 3500 children and women are still held hostage as slaves under Daesh. Every day they die a thousand times."