The 20-year-old spent the second half of last season on loan at Accrington Stanley, featuring on 18 occasions in League Two, before returning to Man United over the summer.
Vitek made a huge impression with his performance in Man United's first friendly of the summer against Rosenborg in July, producing a number of impressive saves in his side's 1-0 defeat.
There had been suggestions that the Czech Republic Under-20s international could be a part of the goalkeeping group at Old Trafford during the 2024-25 campaign, but it has now been confirmed that his development will continue in Austria.
"We'd like to wish Radek the very best for his spell at his new club, where we will be following his progress very closely," read a statement on Man United's official website.
Vitek arrived at Man United from Czech club Sigma Olomouc in 2020, and he has another three years left to run on his contract with the 20-time English champions.
Andre Onana will once again be Man United's number one goalkeeper this season, with Altay Bayindir providing the back-up following his arrival in the summer of 2023.
Tom Heaton, meanwhile, signed a new one-year deal over the summer to remain the number three at Old Trafford, and there have been claims that he could transition into a coaching role for the 2025-26 season.