Bayer Leverkusen striker Schick's header on 42 minutes put the Czechs in front at Hampden Park, before he scored an outrageous second from all of 54 yards out. It meant a disappointing return to tournament football for Scotland, who must now regroup for their showdown with England in Group D on Friday.
Scotland's Stuart Armstrong told the BBC: "We're disappointed with the way the first goal went in, apart from that we defended pretty well, and they showed real quality for the second goal. Not to say we didn't have chances second half, we did, and tried to push. They were clinical. At this level you do need to be clinical."
Scotland suffered a major blow ahead of the match, with Arsenal's Kieran Tierney missing out through injury, while Czech head coach Jaroslav Silhavy named an unchanged XI from the side that beat Albania 3-1 in their final pre-tournament friendly.
A vociferous crowd of 12,000 urged Steve Clarke's Scotland on as they returned to top level international football for the first time since their appearance at the 1998 World Cup -- an absence of five European Championships and five World Cups. And Clarke's men began brightly, with Liverpool's Andy Robertson looking lively down the left and John McGinn having an effort blocked inside the area, but it was Czech Republic who had the match's first big chance as Schick brought a good save out of David Marshall down to his right.
The attempt sparked a Scotland response, with Robertson's cross from the left diverted wide by Lyndon Dykes, who was unable to add to his two goals in 11 appearances for his country. The attacks kept coming, with Robertson -- comfortably his side's best player in the first half -- fizzing a powerful effort towards goal, but it was well tipped over by Tomas Vaclik in the Czech goal.
Scotland were the better side but they fell behind just before half time when they failed to clear a succession of corners, and Vladimir Coufal's cross was met superbly by Schick, who nodded past Marshall to put his side in front.
The setback was a cruel blow to Clarke's men just before the break but not unexpected, with Czech Republic scoring over half their goals in Euro 2020 qualifying from set plays. But following a sustained spell of pressure, Scotland could not keep the Czechs at bay as Schick nodded in.
Clarke brought on Che Adams for Ryan Christie for the second half and Scotland started brightly, with Jack Hendry seeing his effort cannon agonisingly off the bar. Vaclik then had to be alert and claw Tomas Kalas' effort to safety when it looked certain he'd score an own goal.
But Schick's remarkable second on 53 minutes settled the game in some style. Running on to the ball just near the half-way line, Schick sent a stunning, looping strike goalwards and it beat a shocked Marshall to make the game safe. At a distance of 54 yards, the Leverkusen striker's effort stunned Hampden Park and ensured a place in history as the longest-range strike at a men's European Championship or World Cup. It made it the joint-longest range effort across the men's and women's game, with Carli Lloyd also scoring from 54 yards in United States' World Cup win over Japan in 2015.
On his wonder strike, Schick told the BBC: "I saw him [off his line], I checked in the first half when this situation would come. I was checking where he was standing.
"It's always hard to play against us, we have a lot of hardworking players.
"Scotland were a tough opponent. But we were ready for their tactics."
Vaclik was then at his best to deny Scotland a route back into the game, sticking a leg out to deny Dykes' effort inside the area, and Czech Republic negotiated the final moments to open with three important points.
Silhavy said Schick's goal was the kind of effort the player has attempted before in matches and training.
"We know he is a genius and he knows how to finish," Silhavy said. "The second goal was something out of this world. He likes to try that in training and he tried it in one of our previous games as well."
Clarke refused to blame his goalkeeper for conceding the goal.
"If [Marshall] had been on his line he would have caught it but sometimes you have to credit the goalscorer," Clarke told an online news conference after the clash at Hampden Park.
"He produced a marvellous finish and from there it becomes a difficult afternoon. We showed good invention and had chances to get back into the game but the breaks went against us at the wrong time.
"Disappointed but we have to get ready for the next one. We'll look at what we did right and what we did wrong. We didn't come here for a learning experience, we came here to be competitive.
"Sometimes a football match doesn't go your way and today was that day."
Scotland next face England at Wembley on Friday, while Czech Republic take on Croatia at Hampden Park earlier on the same day.