The Scots, who failed to qualify for the tournament in France, went ahead in the 10th minute when Ikechi Anya latched on to a through ball from Kenny McLean and coolly slotted home through the Czech goalkeeper's legs.
The Czechs had dominated possession and nearly took the lead in the eighth minute when Borek Dockal's direct free kick from just outside the penalty area bounced off the woodwork.
"They got a goal from the one chance they had and we had three or four but couldn't finish," Czech manager Pavel Vrba told reporters.
"We didn't really play for four months and it was probably visible."
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The home side, playing without a number of regular players including Petr Cech, forced Scotland keeper Allan McGregor into a number of saves but lacked the final bit of quality in attack.
Daniel Pudil nearly equalised in the 82nd minute when he met a cross from Vladimir Darida but the Scottish keeper made a good save.
"The biggest mistake was we weren't aggressive enough in the last third of the pitch," Czech midfielder Kamil Vacek said.
The Czechs, who finished top of their qualifying group ahead of Iceland, Turkey and the Netherlands, will open the Euro 2016 tournament in a Group D match against Spain. They play Sweden in another warm-up game on Tuesday.
(Reporting by Michael Kahn,; Editing by Ed Osmond)
