The Ghanaian defender, 23, re-joins the Bundesliga side, where he spent the first half of last season before sustaining a knee injury during the Africa Cup of Nations.
Baba signed for Chelsea from another German side, Augsburg, in the summer of 2015 and made 23 appearances during his maiden season at Stamford Bridge.
Schalke are currently third in the Bundesliga.
In another loan move, Nathan has joined Portuguese side Belenenses until the end of the season.
The Brazilian attacker, 21, spent the first half of the campaign on loan at Amiens in France and has now moved to the Portuguese top flight.
Nathan, who signed for Chelsea from Atletico Paranaense in 2015, spent last season with Vitesse Arnhem and helped the team win the Dutch Cup, their first major trophy.
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