The £52million signing from RB Leipzig came off after falling in the penalty area before being substituted for Mykhailo Mudryk in the 22nd minute.
Nkunku is now a doubt to face Liverpool in the opening Premier League match at Stamford Bridge next weekend.
Pochettino gave an update on Nkunku’s condition after the 1-1 draw with Dortmund in Chicago.
He said: “The doctors are checking him and I hope it is not a big issue. He fell in the action which was maybe a penalty and he feels something in his knee but we hope it is nothing big.
“We hope he can be back quickly with the team. We need a few days to assess him.”
An Ed Sheeran concert at Soldier Field over the weekend left the pitch at Soldier Field in poor condition for the match.
Pochettino admitted Chelsea took a risk playing on the surface but was cautious not to be overly critical of his hosts in the United States, adding: “I didn’t see the action but it not about to complaining.
“Always we take some risks because the pitch is not perfect because they are using it for different sports and that is sometimes the risk of the tour, yes.
“But I think it was a bit unlucky in the situation but we cannot complain about the pitch and to blame the pitch for why he suffered the injury. For me it was bad luck.”
Academy striker Mason Burstow’s 90th minute equaliser was the least Chelsea deserved after Marius Wolf scored against the run of play on Wednesday night.
Chelsea end pre-season feeling positive having gone undefeated across all five games, winning the Premier League Summer Series in the process.
Pochettino says Chelsea will be ready when they meet Jurgen Klopp’s side on August 13: “We should be ready. It is not an option.
“There is only one option, to be ready and we are going to be ready. I think today we play a brilliant game, I think it was an exciting game against a very good team like Dortmund.
“I think we deserved to win but it’s not about the result, it’s about the feelings and performance and I think when we scored with Mason at the end it was a relief.
“I think to go back to the feeling, to lose the game was unfair. I think in the end it’s to build something and the feeling after five games on the tour are good.
“Now we need to keep working and evolving our way to play and yes, be ready to start the competition.”
