The Ilava-born centre-back - who had a successful spell on loan with FC DAC in his homeland in the second half of last season - has been named in coach Pavel Hapal's 24-man squad for the tournament.
The Championships take place in Poland later this month and Slovakia are in Group A with England, Sweden and the hosts.
Satka was part of the squad which qualified for the tournament as group winners, with six wins and a draw from their eight matches.
The 21-year-old made his first-team debut for Newcastle against Leicester in the FA Cup in January 2015.