With the suspension effective immediately, Klopp will be in the stands for Liverpool's final home game of the season against Aston Villa on Saturday.
However, the second match is suspended until the end of the 2023-24 season on the condition that Klopp does not repeat the breach.
The 55-year-old was shown a yellow card by Tierney after the Liverpool manager celebrated in the face of fourth official John Brooks following Diogo Jota's dramatic stoppage-time winner in the 4-3 win against Spurs.
Following the game, Klopp admitted that his celebration was "unnecessary" but suggested that Tierney had something "against" his side.
In a statement, the FA said: "Jurgen Klopp admitted that his comments regarding the match referee during post-match media interviews constitute improper conduct as they imply bias, question the integrity of the referee, are personal, offensive, and bring the game into disrepute.
"An independent Regulatory Commission imposed these sanctions following a subsequent hearing and its written reasons can be seen below."
Liverpool sent a letter three days after the match to emphasise that Klopp had not intended to question the referee's integrity.
Klopp also submitted a letter on May 3, saying that the language he used in the post-match interview was "inappropriate" and "driven by emotion".
The Football Association provided a transcript of what Tierney said to the Liverpool boss when he cautioned him.
After being informed by Brooks about Klopp's behaviour towards him, Tierney conferred with VAR to confirm that a yellow card was appropriate.
When distributing the booking, Tierney told Klopp: "Right, I have to show you yellow... it could be red, but I am going to show you yellow. He [VAR] said yellow. We will give you the benefit of the doubt, don't do anything more."
Liverpool are currently sitting in fifth place in the Premier League table, with one point separating them from the top four.