Isakov was shot by assailants near his home in Derbent and was hospitalized in serious condition, the Russian news agency RIA Novosti said.
Russia's top investigating committee is searching for the perpetrator and has not ruled out the possibility Isakov's religion "is among the possible motives," Novosti said.
Ramazan Adulatipov, the acting head of the republic, condemned the attack.
"Dagestan is outraged. Extremists and terrorists don't want a normal, prosperous life for all of us," the agency quoted him as saying.
The area where Isakov lives is a predominantly Muslim and near the Chechen border.
Israel's Foreign Ministry said it was aware of the incident, Israel Radio said, adding, Russia's chief rabbi was chartering a plane to airlift Isakov to Israel as soon as his condition permits.