The dance troop is closely associated with Ramzan Kadyrov, the Chechen leader.
Stavropol, an ethnically Russian city, lies on the northern edge of the Caucasus region, which has seen frequent attacks in a war between Russian forces and separatist fighters.
So far no group has claimed responsibility for the blast, which one official described as an "brutal provocation".
"Someone wants to shake loose the friendly relations between the peoples and republics," regional governor Valery Gayevsky said.
"These forces do not want peace in the Caucasus. But we will put them in their place."
Russia has seen ongoing battles between separatist fighters and state forces in the North Caucasus, and deadly attacks in the republics of Chechnya, Ingushetia and Dagestan are a near-daily occurrence.
In March, Russia was shaken when two female suicide bombers, both from the North Caucasus region of Dagestan, killed 40 people in a pair of co-ordinated attacks on the Moscow metro during the morning rush hour.