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.
“It tore a ligament off the bone and a little bit of the bone away. It’s a nasty one for a goalkeeper, Shamal George had it a couple of years ago and was out for quite a while.
“We tried to do it medically without an operation and rest, but he had a bit of a setback a couple of weeks ago when he had to have an operation and have the bone cut out.
“He’s recovering now and we are looking to just after Christmas before he will be back training with us.
“He has settled in really well since he came to the club and we are really pleased with him.”