Skrtel returns to Slovak training
Skrtel, his team's most high profile player, had been training separately or without the ball this week at the World Cup debutants' base in central Pretoria to strengthen his ankle before Tuesday's Group F match against New Zealand.
Stoch should also be fit for that opening game despite hurting his knee.
The 20-year-old, whose move to Turkish club Fenerbahce from Chelsea was announced on Thursday, had been due to talk to the media after training but instead got straight on the bus.
"It is nothing serious," team spokeswoman Marianna Cizmarova told reporters.
Instead of Skrtel, it was midfielder Juraj Kucka who had an individual session, using a half Swiss ball for exercises to help his own ankle problem. He should be fit for Tuesday but is more likely to be on the bench than in the starting line-up.
Italy and Paraguay are the other teams in Group F.