The German side had asked European football's governing body to investigate whether Drogba was allowed to play in the last-16, first-leg tie on 20 February, following his move from Chinese side Shanghai Shenhua.
However, in a statement on their website, UEFA said: "Having examined all the documents of the case, the Control and Disciplinary Body decided to reject the protest lodged by Schalke."
Former Chelsea player Drogba, 34, agreed to join Galatasaray on 28 January after ending his short stay with Shenhua amid claims he had not been paid his salary.
Shenhua countered that Drogba was in breach of his contract and it fell to FIFA to provisionally clear the way for the Ivory Coast international to make his Galatasaray debut in the 2-1 win over Akhisar on 15 February.
Schalke earned a draw in Istanbul after Jermaine Jones' away goal cancelled out Galatasaray striker Burak Yilmaz's early opener.
The two sides meet in the second leg of the tie on 12 March in Gelsenkirchen.