Llorente picked up a minor muscle problem at Southampton on Tuesday, leading to his half-time withdrawal. He will not therefore be risked at home to West Bromwich Albion on Sunday.
Mateusz Klich and Robin Koch will also miss the game having been given time off at the end of the season. The pair were this week named in Poland and Germany's squads for the European Championships.
Llorente and club-mate Rodrigo will be hoping to be in Spain's 26-man party, but coach Bielsa says his decision was purely about preventing a recurrence of the injury problems which ruined the first half of the centre-back's debut season in West Yorkshire.
"Throughout the first half against Southampton he felt something in his muscle that had he continued he could have got injured where he previously had been before," he explained.
"That's why we decided he shouldn't play the second half od that game, nor on Sunday."
Llorente joined from Valencia in September but was not considered fit enough to make his debut until ealry December. An injury picked up in that game, and another on his return in late January meant it was February 23 before he played 90 minutes for the club but since then he has been hugely influential in Leeds's improved defensive form, starting every match since.
Scotland's Liam Cooper and North Macedonia's Ezgjan Alioski are also due to play in the Championships and it would be a major surprise were England not to select Kalvin Phillips on Tuesday. Illan Meslier has been called up by France's under-21s this summer.
Bielsa hopes all are heavily involved.
"Every decision I've taken, I take it thinking of the player and Leeds United, not thinking in other aspects," he said.
"I hope it goes well for them with their national teams and I hope as many Leeds United players as possible pariticipate for their nations.
"These decisions for Klich, Llorente and Koch, they're not linked to the possibilities they have with their national teams because I have no information about that.
"The decisions on Koch or Klich, I had no way of knowing what was going to happen with their national teams and the same with Llorente.
"In no way did I want to risk Llorente having another muscular problem.
"Nor did I want to take a risk of a slight problem in his hip to get worse for Koch. I considered the amount of minutes Klich had played in the last three seasons and the effect the excess of competition produced in him.
"It made me think once he had recovered his level he deserved a rest like the one I gave him."
Bielsa also paid tribute to the professionalism and abilities of Pablo Hernandez and Gaetano Berardi, who will leave the club at the end of the season.
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