"It will be held in November, after the (2014 Winter) Olympics," Anatoly Pakhomov said in Moscow.
Last year local media reported, citing sources within the Russian Automobile Federation, that work on the £127 million project had been stopped.
Pakhomov, however, dismissed any doubts about the construction being completed on time.
"The circuit's construction is being closely monitored by the regional government. Everything is going according to plan," he said. "If we had any problems we would have asked for help from other regions."
In 2010, Russia signed a seven-year deal with Formula One supremo Bernie Ecclestone to stage a Grand Prix race in the Black Sea resort from 2014 until 2020.
Sochi hosts the Winter Olympics in February 2014.