Alina Yakimkina, 21, died during a Russia Cup biathlon race in Tyumen on Saturday in what Mutko described as a "huge tragedy".
Yakimkina, competing for the Republic of Udmurtiya, suddenly fell to the ground 700 metres from the finish of the individual race.
According to the autopsy, acute heart failure was the cause of death.
"I want to offer my condolences to Alina's relatives and loved ones. This is a huge tragedy and the investigation will be carried out mainly by the Ministry for Sport," Mutko told Reuters in a telephone interview on Monday.
Biathlon, which combines cross-country skiing and shooting, has been hard-hit by doping scandals in recent years but Mutko dismissed allegations that Yakimkina could have been taking performance enhancing drugs.
"I have already read such accusations and points of view. Everyone is trying to guess what happened.
"You have to understand that there is absolutely no point using performance enhancing drugs in these kind of events. This was not a selection event for the Russian national team, but just an ordinary leg of the Russian Cup.
"The most important thing is to wait for the final reports concerning the cause of death, which will be carried out by experts, who will try to explain why this happened. We will make sure this happens," said Mutko.
According to the Russian sports minister, more attention needs to be paid to the health of competitors in sport.
"On the whole, this system has been working well over the last few years. At every event, a medical team is on stand-by, while the sports men and women undergo serious examinations if they want to compete.
"However, medical examinations of sports men and women in Russia's regions should be carried out regularly.
"We are now trying to find out how this process worked in Udmurtiya, while we will also be paying more attention to the regions of our country concerning the question," Mutko added.
(Reporting by Dmitriy Rogovitskiy; Editing by Ken Ferris)
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