Mutko was quoted in January saying he wanted to change the structure of the sport ministry to create a position in the department that would "exclusively concentrate on fighting against doping."
It had been thought that the new job would be a deputy minister yet, after appointing Zhelanova, Mutko claimed he had been misinterpreted.
"She [Zhelanova] used to be in charge of the sport ministry's department for anti-doping safety and interdepartmental cooperation. The new appointment is a promotion for her," Mutko told the All Sport agency.
"After the recent anti-doping stories, I said I wanted to give the post to a deputy minister, but I was not correctly understood. I cannot make a deputy minister concentrate only on anti-doping.
"In the future, I want to have a deputy who will look after questions regarding education, science and the fight against doping. The appointment of Natalya Zhelanova is a move in that direction," Mutko added.
The issue of doping in Russian sport re-emerged in December, following a three part documentary broadcast by the German television channel ZDF/ARD, which alleged widespread drug use.
The Russian Anti-Doping Agency announced in January that three Olympic walk champions, Olga Kaniskina, Valery Borchin, Sergei Kirdyapkin, had all been suspended for doping infringements, as well as 2011 world champion Sergei Bakulin and silver medalist Vladimir Kanaykin.