The 19-year-old joined the Gunners on a long-term deal from Brazilian outfit Sao Paulo in the summer, and he has impressed during spells with both the senior side and youth set-up this season.
Marquinhos scored and provided an assist on his Europa League debut in a 2-1 win against FC Zurich in September, and he has made a further five senior appearances for the Gunners in all competitions.
The winger has also made an impression at Under-21s level, contributing with four goals and two assists in five Premier League 2 outings.
However, Marquinhos is not deemed a first-team regular at present by manager Mikel Arteta, and the teenager will now test his mettle in the Championship with promotion hopefuls Norwich City, where he will wear the No.13 shirt.
Speaking to the Canaries' official website on his arrival at Carrow Road, Marquinhos said: "I'm really happy to arrive here in Norwich and very excited to play my first game.
"I've learnt a lot as part of my adaptation here in England. It's totally different to Brazil. It's more intensive but I'm adapting well in order to help Norwich.
"I'm also really happy to get to know a new club, a new culture and a new city. The fans can expect that I'll show desire."
Head coach David Wagner added: "We're delighted to have been able to add Marquinhos to our group. He is a young and exciting wide player, who wants to learn and further continue his development.
"I'd like to thank both Arsenal, for their in trust in allowing the deal to happen, and Stuart [Webber] for getting everything sorted so quickly.
"We now look forward to welcoming Marquinhos to our first-team group ahead of the remainder of the season."
Marquinhos becomes Norwich's first signing of he January window and moves to Carrow Road shortly after the Canaries allowed Todd Cantwell to join Rangers on a permanent basis.
Norwich currently sit sixth in the Championship table, just inside the playoffs on goal difference, and Marquinhos could make his debut for Wagner's side when they play host to league leaders Burnley on Saturday.