Chilwell started for England in Saturday's 1-0 loss to Brazil and Tuesday's 2-2 draw with Belgium in friendlies, his first appearances for the national team since a hamstring injury in September sidelined him for over three months.
"He wasn't alright to train today so we will need to assess him ahead of tomorrow," Pochettino told reporters before Saturday's Premier League home clash with Burnley.
"I was a little bit surprised that he started two games for England and now he's had a knock, but we need him available to play for our club."
Chilwell also suffered a knee injury earlier this month and has not played for Chelsea since the 2-2 draw at Brentford on March 2.
Chelsea, who have nine first team players out injured, including forward Christopher Nkunku and captain Reece James, also lost midfielder Romeo Lavia for the season due to a hamstring injury on Thursday.
"Of course he's not happy because he has only played 30 minutes as a new player for the club ... it's a shame but sometimes these things happen in football," Pochettino said about Lavia.
The Argentine added that 11th-placed Chelsea would not underestimate Burnley, who are in 19th place battling to avoid relegation.
"It's not just about points because you can see the potential of their team," he said. "It's going to be difficult. They are a team that play with freedom and are very physical."
