The request will now be forwarded to an arbitration body at the Norwegian Sports Confederation, which will rule on the sanction to be imposed on the former Olympic gold medallist.
If the Agency's request is upheld then Johaug would miss the start of the next World Cup in addition to the current one but could be back for the Pyeongchang Winter Olympics in February 2018.
"I am glad that (the prosecuting committee within the Anti-Doping Agency) believes in what I have said," Johaug said in a statement sent by her lawyer. "But I do not understand that what has happened can justify 14 months of suspension."
"I am now looking forward to seeing the case before the arbitration body and I hope that it can happen as quickly as possible," said the 28-year-old skier, who has already been suspended for two months pending a final sanction.
Johaug tested positive for traces of the prohibited anabolic steroid clostebol, banned by the World Anti-Doping Agency (WADA), during an out-of-competition control on September 16.
The steroid was contained in a lip cream called Trofodermin, which she used to treat burns during a training session at altitude in Italy in late August.
National ski team doctor Fredrik Bendiksen, who has insisted he did not realise the cream contained clostebol, has taken full responsibility and resigned from his post in October.
"As a high-level international athlete, Therese Johaug is subject to strict international regulations," Anstein Gjengedal, an official at the Norwegian Anti-Doping Agency said in a statement.
"The athlete's responsibility for what he or she ingests has been established in a number of doping verdicts at the national and international level," he said.
The anti-doping agency has requested that the suspension be applied retroactively, from October 18.
An immensely popular athlete in her winter sports country, Johaug won relay gold at the 2010 Vancouver Olympics, and silver in the 30km freestyle and bronze in the classic 10km in Sochi 2014.
This is the second incident to embarrass the Norwegian Ski Federation this year. At the end of July, men's cross-country skier Martin Sundby was suspended for two months and stripped of his 2014-15 overall World Cup and Tour de Ski titles for unauthorised use of ventoline.
The Federation had also assumed the responsibility, having failed to request an authorisation for the use of the anti-asthmatic.