After opening addresses from beleaguered FIFA president Sepp Blatter and Jacques Rogge, the president of the International Olympic Committee, Calmy-Rey warned FIFA to waste no time in getting its house in order.
She hoped also that it would not be long before women were seen among the members of the 24-man executive committee.
FIFA has been rocked by a series of scandals recently and Calmy-Rey urged the governing body to "take seriously the many criticisms voiced about corruption and a lack of transparency.
"It is important you examine them swiftly and take the necessary measures to reform your governance. It is of the utmost importance because your organisation should be an example not only to young people but to the world at large.
"What is important is to restore full confidence in the organisation; let not money spoil your ideals," she added.
"This is not the time for a catenaccio defence but time for a courageous offensive on the pitch of transparency to reclaim integrity, respect, tolerance and team spirit.
"FIFA is important to Switzerland so I wish you the energy necessary to overcome the many challenges which face you."
SHAKY PYRAMID
Blatter had earlier opened the Congress, warning of the dangers the governing body is facing.
Welcoming FIFA's 208 delegates at a ceremony featuring jugglers, folk dancers and singer Grace Jones, Blatter said he would speak in more detail about the problems facing FIFA before the business part of the Congress starts on Wednesday.
However, he warned: "I thought we were living in a world of fair play, respect and discipline but I must unfortunately say this is no longer the case because our pyramid, the famous FIFA pyramid, is suddenly unsure on its basis and there is danger."
Two Confederation presidents, Mohamed Bin Hammam of Asia and Jack Warner of CONCACAF, have been banned from the Congress after being suspended from all football related activity on bribery allegations.
Blatter continued: "Tomorrow, dear friends, when I open the Congress agenda, I will speak of the danger lurking and I will tell you how we can fight this threat of danger, how our sport can play its role in bringing people together in the future.
"Tonight we want to meet in a festive atmosphere, but to keep the fascination of our sport we must respect it, it's up to all of us. It's our game, all of us have a duty to protect this sport and this is what we want to do. I am certain we will achieve this."
Blatter is expected to be re-elected by acclamation for a fourth term on Wednesday, although a number of associations including England and Scotland could call for the election to be postponed in the light of the corruption claims.
Rogge recalled the IOC's own cash-for votes crisis over the 2002 Salt Lake City Winter Games.
Appearing to lend support to Blatter, who sits on the IOC as FIFA president, he told delegates: "FIFA is now facing allegations and controversy.
