The Orthdoxo Church didn't have a pope. Therefore, no reformation.
The Reformation was based on:
1) Ongoing sales of indulgences so that Rome had more money. It created theological and nationalist resentment.
2) Obstensible reason for various taxes, tithes, and other money sent to Rome was for crusades to liberate Constantinople/Jeruslaem that never happened.
3) Discrediting of the Papacy by the Great Schism.
4) Ongoing scandalous behavior by the Popes damaging the prestige of the Papacy.
5) Rising nationalism that created resentment that the national church was lead by a "foreign prince".
6) A desire to steal Church lands and money by the kings of Europe.
None of these apply to the Orthodox church.
There was no single bishop in charge of the Orthodox so any corruption or monetary issues were local affairs that did not discredit the Church as a whole. No Great Schism that damaged the unity of the Orthodox Church. And since the Orthodox areas had the doctrine of caesaropapism that prostrated the church to powerful rulers and in Russia a strong tradition of the ruler acting like he owned everything, princes and tsars could take anything they like without having to worry that some bishop would opppose him.
So there was almost none of the reasoning for the Reformation.
In contrast, the "Third Rome" of Moscow saw the need for keeping a unified, Orthodox Church that served the rulers of Moscow in their attempt to consolidate and unite the remaining independent Orthodox lands in Russia around the same time. Moscow was not going to tolerate independent reformers who would put their theological whimsies ahead of their need for a united doctrine/church.
Now, on a related level, there was an ongoing anti-clerical forment in Latin Christianity that would erupt from time to time by reformers like the Waldensians, or extreme poverty advocates like the Fraticelli. However, by themselves they were insufficient for the reformation, at least the reformation we got IOTL. Although I can't name any off hand, I would not be surprised if the Orthodox church had basically the same kind of movements as these. But without the above, they were insufficient to gain adherence.
Another thing is that the support for the Reformation was largest in the new middle class. These people had the wealth and free time to devote to thinking about religious issues for themselves at the same time the printing press made the bible available to them in their own language. The Orthodox lands lacked such a relatively large bourgeosie population.