The 18-year-old scored 16 goals in 17 starts for Boro’s academy last season before making his senior debut as a late substitute in a 4-3 defeat to Leeds United in April.
Speaking after the game, Boro head coach Michael Carrick said: “It was great to get Ajay on – giving youngsters opportunities is what this club is all about and what we love doing as a coaching team. Obviously we want to keep a lid on it a little bit as well.
“It’s always great for me to be able to give young lads an opportunity and we thought he deserved one tonight. He’s a goalscorer and he’s proven that over the course of the season. At this stage of the season and in the game, it was kind of, roll of the dice a little bit. He had a little sniff to almost get one as well after we’d got one back.”
Matthews made his second appearance in a 4-1 win at Cardiff City five days later. At the end of May, he represented England at under-18s.