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.

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 2012 Targett launched his career as a male model, signing with Melbourne editorial agency Chadwick Models.