Chelsea were hit with several injury problems early in the season, including captain Reece James who suffered a hamstring injury on the opening day and Christopher Nkunku, who needed knee surgery.
Mudryk, who cost Chelsea an initial 70 million euros in transfer fees in January, is now the ninth player to be sidelined. The club did not reveal the nature of his injury.
"He won't be available for tomorrow. He is a player we hope to help perform in the way we believe he can perform," Pochettino told reporters before Friday's home game against Luton Town.
"It's not a big issue, we need to wait one week or maybe a few days."
Carney Chukwuemeka went off injured having scored in the 3-1 defeat at West Ham on Sunday and the 19-year-old underwent knee surgery, but the recovery time should be shorter than first feared.
"It is not an issue for months, maybe weeks," the manager said.
"I think it is a bit unlucky in some issues like with Carney on Sunday. That is football. It is true, a little bit unlucky with many of the injuries, but I am positive."
The injury list also includes Wesley Fofana, Armando Broja and Benoit Badiashile and Pochettino put most of them down to "bad luck".
"Nkunku and Carney or Fofana. How can you control? It's not about training or methodology. It sometimes happens," the Argentine explained.
"In some others, many factors can influence. It's tough to talk in general because situations are different. In general, you can talk about bad luck or (a) bad training session - for sure it is bad luck in Carney, Broja, Fofana, Nkunku."
With so many injuries, the manager spoke about the possibility of new signings.
"We need at least one keeper. We have very talented young keepers but they need time," Pochettino said.
"We were talking about one offensive player. If we can add the right profile, yes, but not to bring players so we can add more and to stop the evolution of some young guys."
There was some good news for Chelsea as British record signing Moises Caicedo could make his first start for the club. But fellow midfielder Romeo Lavia, who was signed from Southampton, may need to wait.
"Mo (Caicedo) yes, is ready to start. Lavia no. He needs a few weeks to be ready to be involved with the team," Pochettino told reporters on Thursday.