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 so far for the Reds' first team following his deadline day loan move from Juventus.
The Brazilian's inactivity over pre-season meant he arrived on Merseyside lacking in match fitness, and it was reported last week that he had been placed on a rigorous regime in order to get him up to speed.
After being overlooked for Brazil's squad for the September internationals, Arthur decided against going on holiday over the next couple of weeks, 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 over the summer as a player-coach for the youth side.
The young Reds fell behind to a late Tahvon Campbell goal at the Crown Oil Arena, before Oludare Olufunwa picked up two bookings and Liverpool ended the match with ten men.
Liverpool have now lost both of their opening Papa John's Trophy group stage matches 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 have recently appointed Roberto De Zerbi as Graham Potter's successor, travel to Anfield.