Arthur played just under an hour of Liverpool Under-21s’ 1-0 defeat to Rochdale in the Papa John’s Trophy on Tuesday evening.
The midfielder has made just one appearance for the Reds’ first team since his deadline day loan move from Juventus.
The Brazilian’s inactivity in pre-season meant he arrived on Merseyside lacking match fitness, and it was reported last week that he had been put on a strict regime for speed.
After being overlooked in Brazil’s squad for September’s internationals, Arthur decided against taking the next two weeks off, and he started for Liverpool’s U21 side in the Papa John’s Trophy on Tuesday.
He was replaced around the hour mark by former senior midfielder Jay Spearing, who returned to the club in the summer as a youth team player-coach.
The young Reds fell behind to a late Tahvon Campbell goal at the Crown Oil Arena, before Oludare Olufunwa earned two bookings and Liverpool ended the match with ten men.
Liverpool have now lost both of their opening matches in the Papa John’s Trophy group stage following a 1-0 defeat to Salford City. They next face Accrington Stanley on October 18.
Arthur could make his first Premier League appearance on October 1 when Brighton, who recently appointed Roberto De Zerbi as Graham Potter’s successor, travel to Anfield.