The accident happened while the soldiers were cleaning a nitrogen gas tank during routine maintenance, Russian news agencies quoted a defence ministry official as saying.
The ministry did not disclose details of the accident, saying only that it was caused "by the officers' failure to follow safety procedures."
The Plesetsk Cosmodrome, located about 800 kilometres (500 miles) north of Moscow, was developed by the Soviet Union as a launch pad for its intercontinental ballistic missiles.