Fati's injury means he will be added to a growing list of key Blaugrana players to miss out on the La Liga encounter, including Lionel Messi.
After Friday's training session Barcelona released a statement confirming Fati's injury and indicating the length of time he will miss is currently unknown.
"After the session it was announced that Ansu Fati will miss the game on Saturday at Getafe with a tendon problem in his right knee," the statement read.
"His recovery will dictate his return to action."
With Messi missing for the season's opening month, Fati surprisingly helped fill some of the void by contributing two goals and an assist in five La Liga matches.
But the 16-year-old has now been forced to the sidelines as Barcelona look to improve on a stuttering start to the 2019-20 campaign without several key players.
Additionally, he could be selected for the U17 World Cup by Spain. The tournament runs from October 26 to November 17 in Brazil, though there are reports Spain could instead fast-track Fati into their U21 squad.
"I'd like him to be with us," Barcelona manager Ernesto Valverde said of the teenager. "If he goes with the Under-21 team it would be for the international break, for the Under-17s it would be longer.
"We'll have to wait and see what decision the confederation makes so there isn't much else to say. We'd like him to be away for as little time as possible."
The Blaugrana currently are in sixth in the La Liga table, having won three, drawn one and lost two of their opening six matches.
Part of the reason for the slow start has been the absence of Messi, who has played a total of just 90 minutes over two league matches thus far.
However, Messi suffered a groin injury in Tuesday’s 2-1 home win over Villarreal, with Valverde unsure how long the 32-year-old will be out.
"I don't know how long he's going to be out, hopefully he'll be back with the team soon. It's not a serious injury so let's wait and see what he looks like today and going into next week.
"If he plays we have certain strengths, if he's not we're missing a top-quality player who makes a huge difference. We have other resources to take games on and we've done that. It's a setback but we can only keep going."
Messi and Fati aren't the only injury concerns for Barca, however, with Jordi Alba and Samuel Umtiti also out for Saturday's game against Getafe.
Umtiti has yet to play this season as he continues his recovery from a foot injury, while Alba has missed Barcelona's last two matches with a hamstring injury.
Barcelona have only won six of their last 14 La Liga away games without Messi, losing six times and drawing twice.
They go to Getafe on the back of a run of seven straight away games in all competitions without a win, while their hosts are unbeaten in six matches and Valverde is expecting a tough challenge at Coliseum Alfonso Perez.
"They're a solid team, it's hard to cope with their pressure," he said. "Very good in attack with players that come through to put you under pressure.
"It was hard to win there [2-1] last year, we played a good game, but it was difficult. They always make chances at home and don't give away many.
"Sometimes it's like we have to win as soon as possible to stop a problem. We want to win the points always. We haven't won away or played well away, in general we haven't played well away and we need to focus on that.
"Sometimes the score works out and sometimes it doesn't. You need to play good football, and this is what gets results."