The 18-year-old stopper made an appearance for the first team against Tranmere Rovers in pre-season before suffering the injury during training.
A member of the FA Youth Cup-winning squad last term, the Czech is hoping to return to action with the U23s in early 2020.
U23s goalkeeping coach Mark Morris told Liverpoolfc.com: “Veet went up to train with the first team in the first week back of pre-season and played against Tranmere Rovers.
“He was doing really well and enjoying himself and then he got an injury in training when he took a knock on his elbow from close range.