Švento made his international debut for Slovakia in the friendly match against Malta on 15 August 2006.
During summer 2007, he went to an English club Derby County for a trial and to take a look at the facilities there. Seemingly, more English based clubs were interested. However, this interest ended as he damaged his knee ligaments after returning to Prague. He has undergone surgery and has been out for almost a year.
On 16 June 2009, Švento joined Red Bull Salzburg after signing a three-year contract for a transfer fee of €2 million.