In 2006 and in his home town of Melbourne, Targett competed in the 50-metre butterfly, finishing second and placing above more experienced countrymen Michael Klim and Matt Welsh. Targett was later disqualified for twitching before the starter's signal.
Targett's second international meet was at the 2008 Olympics in Beijing, China, capturing a silver in the 4×100-metre medley and a bronze in the 4×100-metre freestyle relay, both in new Commonwealth record time. He also finished 7th in the individual 100-metre freestyle.
Matt Targett's first world championships came in 2009 in Rome, Italy, he swam 4 races on day one, and thus not looking in peak form in the 4×100-metre freestyle relay, with the absence of Ashley Callus and Eamon Sullivan, Australia was never in medal territory. Everything turned around on night 2, when he captured a silver in the 50-metre butterfly, with a terrific first 35 meters, he started to even up and he was touched out by Milorad Čavić by six hundredths. On the final day of competition he anchored the 4×100-metre medley relay to bronze.
In 2010, amidst sickness, Targett finished 5th in 50-metre butterfly and 14th in the 100-metre freestyle at the Telstra Australian Swimming Trials and failed to qualify for a second Commonwealth Games.
On night 1, James Magnussen was the starter for the Australian relay team for the 4×100-metre freestyle relay, setting a swift 47.49 to get a large lead over Michael Phelps and Alain Bernard. Targett swam the second leg to extend the lead, Australia lead the whole way changing over to the 3rd leg with Matt Abood, finishing with sprinting veteran Eamon Sullivan holding off a strong finish by France. Night 2 brought more success, capturing silver again in the 50-metre butterfly behind César Cielo, his compatriot Geoff Huegill finishing with the bronze. In the lead up to these championships, Targett developed a reputation at his club for his intensive strength regime outside the pool.
Targett was only selected for the 4×100-metre freestyle relay alongside countrymen James Magnussen, Eamon Sullivan and James Roberts. As favorites leading up to the London Games, the team was dubbed "Weapons of Mass Destruction" by the Australian media. The morning team, of which Targett and Sullivan were not part of, qualified fastest for the final. In what has been named by some to be "darkest day" in swimming in recent memory, the team came only 4th behind France, the USA and Russia. After a slow start by Magnussen, Targett as second swimmer held on to gain a position, while Sullivan, who had the fastest split of the team retained third place, however anchor James Roberts was unable to hold off a Russian powerhouse team, and was pipped at the wall and finished in 4th position.
In a surprise decision by the Australian coaching staff, Targett was selected to swim the butterfly leg of the 4×100-metre medley relay in the heats. Targett swam a 51.30 and as a result was placed into the team for the final along with Hayden Stoeckel, Christian Sprenger and James Magnussen. Australia cinched bronze in the final, behind the US who claimed gold and only 0.32 of a second behind Japan.
In 2012 Targett launched his career as a male model, signing with Melbourne editorial agency Chadwick Models.