He played in all five of his side's September games, helping the All Whites to four wins and a draw to put them at the top of the Principality Premiership table.
Matthew played his junior and youth rugby at Bridgend Athletic and has also benefitted from being part of the WRU Ospreys academy.
Simon King coached him within the Wales Under 18 set-up for the past two seasons.
King said, "I'm delighted that Matthew has been recognised for his performances and that he's already making his mark in the Principality Premiership.
"A number of very talented players are now flourishing in the Premiership, even at this young age - Tom Prydie, George North, Ashley Beck and Kristian Phillips last season and now Matthew and Eli Walker at Swansea amongst others in the Premiership.
"These follow a long line of players who have come through the Premiership as a stepping stone to greater things. Only a few seasons ago, Morgan Stoddart, Lee Byrne, James Hook and Jason Tovey were making headlines and winning these awards in our semi-professional competition.
"Matthew is small in stature but I believe his rugby nous and technical ability, along with a tremendous attitude could take him a long way in the game."
Morgan added: "I'm chuffed with how things are going so far this season, and to get this award. It's been a step-up to play in the Premiership but the Swansea players and coaches have helped me a lot and I feel I'm learning all the time from playing with and against better players.
"My ambitions for this season are to win the league with Swansea, to get into the Wales Under 20 squad, and if I play well, I'm hoping to get a few games for the Ospreys."
Matthew Morgan factfile:
Born: 23.4.92, Basingstoke
Position: Outside half
Most admired player: Jonny Wilkinson
Biggest influences: My family and coaches who have all been very supportive
Education: Brynteg Comprehensive, currently a HND student in sports performance and coaching at Neath College
International honours: Wales Under 18
Other sports played: Snooker, school football