Muslera started his professional football career with Montevideo Wanderers in 2004, having come through the club's youth system. After impressive performances for Wanderers, giants Nacional opted to take him on loan in 2006.

Despite only playing at Nacional for a short time, Muslera's performances saw him linked with some of Europe's biggest clubs such as Benfica, Juventus, Lazio and Arsenal.Muslera joined Lazio at the close of the 2007 summer transfer window for €3 million as a replacement for the retired Angelo Peruzzi and after plans to sign Juan Pablo Carrizo were delayed due to the non-EU status of the Argentine. Muslera was signed by the Roman side to become the new first choice goalkeeper ahead of veteran Marco Ballotta.

Muslera made his debut for Lazio in a 3–1 home win against Cagliari on 16 September 2007, and made four more consecutive starts, the last which was a disastrous performance in Lazio's 1–5 home loss to Milan on 7 October, a match in which he was at fault on four of the five goals Lazio conceded. That result saw him benched in favour of 44-year-old Marco Ballotta. Muslera remained as the second choice for the remainder of the season, making only four more league appearances and none in the UEFA Champions League. He did however play all of Lazio's remaining Coppa Italia matches, putting in good performances.

Muslera started as second-choice keeper for the 2008–09 season behind new signing Juan Pablo Carrizo but regained the starting spot in January 2009 following a run of poor form by Carrizo, coupled with conflicts with team management. Muslera's first starting appearance in the league this season saw him make several saves in a 3–1 loss to Sampdoria, including blocking an Antonio Cassano penalty. Further impressive performances in away wins over Napoli and Genoa, as well as in his first ever Derby della Capitale, saw Muslera regain a considerable amount of faith he had lost the previous season.

Known to the Lazio fans as castorino, or the "little beaver", Muslera was also an integral part of the club's successful Coppa Italia campaign, making decisive saves against Milan and Juventus as Lazio reached the final for the first time in five seasons. In the final on May 13, 2009, Muslera saved two penalties as Lazio emerged victorious 6–5 in the shootout after the match ended 1–1 in extra time.

The Uruguayan's impressive season saw him cement his position as the Roman club's first choice in the 2009–10 season, despite the arrival of Argentine keeper Albano Bizzarri on a free transfer. Muslera played in goal as Lazio opened the season with a 2–1 win over Inter in the 2009 Supercoppa Italiana, played in Beijing.

Muslera had been called up for the Uruguayan national team on numerous occasions, but did not earn his first cap until October 10, 2009, when he started in Uruguay's 2–1 away win over Ecuador. The match was Uruguay's penultimate qualifier for the 2010 FIFA World Cup in South Africa. He made his FIFA World Cup debut against France on June 11th, 2010, Uruguay's opening game of the tournament and the second game on the opening day of the 2010 FIFA World Cup. He kept a clean sheet during all 3 of Uruguay's group matches (0–0 against France, 3–0 against South Africa, and 1–0 against Mexico). Muslera was decisive in the quarterfinal match against Ghana, when he saved two penalties at the penalty shootout.

Espaňol:
Nacio en Buenos Aires, Argentina. Debutó A los trece años recaló en el Montevideo Wanderers Fútbol Club donde jugó en las categorías inferiores. Debutó en la Primera División Profesional de Uruguay en el Campeonato Uruguayo de Fútbol 2004, el sábado 6 de noviembre de 2004 frente al Club Atlético Peñarol, partido en el que Wanderers cayó derrotado por dos tantos a uno.

En el año 2006 fue cedido al Club Nacional de Football disputando la Copa Libertadores 2007. Ese mismo año fue traspasado a la Società Sportiva Lazio de Roma, que juega en la Serie A italiana, por 3 millones de euros.

En 2003 integró la Selección Sub-17, bajo la dirección técnica de Jorge Da Silva, y jugó en el Campeonato Sudamericano Sub-17 de Bolivia. Allí la Celeste integró el grupo A (con Brasil, Chile, Venezuela y Ecuador) y con 3 triunfos y una derrota clasificó, detrás de Brasil, al cudrangular final del torneo (que completaron Argentina y Colombia). Argentina resultó campeón del torneo y Uruguay obtuvo la 4ª posición, quedando, entonces, eliminado del mundial que se jugó ese mismo año en Finlandia. En este torneo, Muslera jugó solamente en el partido contra Brasil en la primera fase. En los restantes 6 partidos fue suplente de Sebastián Sosa.

Muslera previo a un partido con la selección uruguaya.

En 2005, integró la Selección Sub-20, bajo la dirección técnica de Gustavo Ferrín y jugó el Campeonato Sudamericano Sub-20 de Colombia. Allí La Celeste integró el grupo B (con con Brasil, Chile, Paraguay y Ecuador) y con 1 triunfo y 3 empates clasificó en tercer lugar al hexagonal final del torneo (que completaron Colombia, Brasil, Argentina, Chile y Venezuela). Colombia resultó campeón del torneo y Uruguay obtuvo la 5ª posición, quedando eliminado del mundial que se jugó ese mismo año en Holanda. Muslera fue titular en los 9 partidos.

Fernando Muslera empezó a ser citado por Oscar Washington Tabárez, director técnico de la Celeste, para los últimos partidos de la eliminatoria para el mundial 2010, debido a que no resultaban totalmente satisfactorias las actuaciones de sus predecesores: Fabián Carini, Sebastián Viera y Juan Castillo. Su debut fue en el penúltimo partido, en Quito, contra Ecuador. En cuartos de final paro dos penalties en la serie contra Ghana, dandole el pase a su equipo a las semifinales.