Summary: Yes, but "only" pillaging and minor skirmishes in Moravia.
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Prelude: Before their maximum European conquest extent of 1241, while Mongols were determined to conquer the whole Europe, they had decided to conquer individual states step by step. Mongols were very competent at scouting their future targets. Apart from learning geography and raw manpower they had also mapped the political climate of local states, strategical marriages as well as feuds of local rulers. They had decided to split their armies into two and simultaneously attack Hungary and Poland.
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So why did they decide NOT to go for an all-out attack of the kingdom of Bohemia (KoB)? Possible reasons:
Mountainous borders. Mongolian army was heavily reliant on fast cavalry. With the exception of east Moravian border there were mountains all around the border of KoB. Unlike in Poland or Hungary where there is a lot of plains.
Venceslas I., the king of KoB at the time was well aware of the grave threat and ordered to improve fortifications as well as to block and guard mountain passes.
Venceslas I. managed to keep his kingdom quite stable. There were some quarrells with Austria, true, but no big deal to the subjects of KoB and Venceslas had at least a formal backup of either the HRE emperor Friedrich II. or the pope Gregor IX. in various phases.
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Battle of Legnica: Henry II. the Pious, the ruler of Poland and Silesia and also Venceslas' brother-in-law fought Mongols on 9th April 1241. Venceslas tried to reach him in time with his even stronger army but was too late. We can only guess what exactly was the reason. Was Henry too reckless? Was Venceslas too hesitant to go into the battle ASAP? Did Mongols manoeuver Henry into an unavoidable conflict before Venceslas could join the fight? In a later letter to the roman king Konrad IV., Venceslas writes: "...we were so near the duke, that a day after his fall we could have arrived to him with all our might, but alas, he did not ask us for advice nor help; he decided to fight them and so he ruefully perished."
In any case, the Mongolian army scored a decisive, yet a pyrrhic victory in both Poland and Hungary. They suffered heavy losses. Vencelas was a day of march away, ready to retaliate and in a full-scale battle he would have probably won. The Mongols decided to retreat from Poland and join both armies in Hungary. They decided to go through Moravia where there was a weak garrison. They couldn't go through Bohemia - Venceslas with his army was blocking their way on the Bohemian-Silesian border.
The Mongolian army entered Moravia through the northern mountain passes but then kept mainly to the river Morava and flatter regions of Moravia. They massacred inhabitants, burned down their villages, destroyed monasteries, pillaged along the way. Some important places of conflict were an unsuccessful siege of Opava, successful razing of Bruntál, long unsuccessful siege of Olomouc defended by the king's main Moravian defence unit of 8000 infantry and riders, unsuccessful siege of Brno.
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There are Moravian folk tales still recalling the Mongolian invasion to this day. There is a kind of gingerbread pastry called Štramberk ears in rememberance to trophies taken by Mongols - ears of slain enemies. By baking these, people celebrate the lives of those Moravians spared such a gruesome fate.
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Sources:
Czech:
Petr Hora: Toulky českou minulostí II. (1197-1526)
František Adámek: Tataři na Moravě
English:
