Ryan spokesman Brandon Buck wrote a pithy email in response: "We're Not Gonna Play It anymore."
Snider says in a statement that he does not support Ryan and denounced use of the song, an anthemic 1984 hit for the glam metal band.
It joins a long list of songs that musicians have asked politicians to stop using.
Most recently, the rock band Silversun Pickups asked likely Republican nominee Mitt Romney to stop using the song "Panic Switch" last week.
"We don't like people going behind our backs, using our music without asking, and we don't like the Romney campaign," Silversun Pickups lead singer Brian Aubert said in the statement.
The campaign said the song's use was completely inadvertent.