Versatile veteran Daly, who was on his third Lions tour, suffered the injury in Wednesday's 52-12 victory over the Queensland Reds having been brought into the starting side just before kickoff when fullback Hugo Keenan fell ill.
Daly's ability to cover the centre, wing and fullback makes him especially valuable on tour and his late call-up in Brisbane was his 11th straight inclusion in a Lions matchday squad going back to the start of the 2021 tour of South Africa.
Farrell, who won the last of his 112 England caps at the 2023 World Cup and announced in early 2024 that he was stepping away from international rugby, will join the squad for his fourth Lions tour, looking to add to his six test caps.
"It is heartbreaking for the group that Elliot's tour is over. He is a Lions legend who has added so much to the group on and off the field over the past few weeks," Andy Farrell said in a team statement.
"Owen will now come in and add to our options and bring his own Lions experience to the group."
Farrell named a third captain in three matches for the clash against the New South Wales Waratahs on Saturday with Irish lock Tadhg Beirne following tour skipper Maro Itoje and fellow-Irishman Dan Sheehan in leading the side out.
Keenan will start at fullback with another option for the number 15 shirt, Blair Kinghorn, named on the left wing having arrived in Australia late on Monday after helping his French club Toulouse to the Top 14 title.
Young English loose forward Henry Pollock returns to the side and will play at blindside flanker in a back row also featuring number eight Ben Earl and openside Josh van der Flier.
Fin Smith, who started at flyhalf in the loss to Argentina in Dublin two weeks ago, gets another shot at the playmaking role in a halfback partnership with his England teammate Alex Mitchell.
Lions team:
15–Hugo Keenan, 14–Mack Hansen, 13–Huw Jones, 12–Sione Tuipulotu, 11–Blair Kinghorn, 10–Fin Smith, 9–Alex Mitchell, 8–Ben Earl, 7–Josh van der Flier, 6–Henry Pollock, 5–James Ryan, 4–Tadhg Beirne (captain), 3–Finlay Bealham, 2–Luke Cowan-Dickie, 1–Pierre Schoeman. Replacements: 16–Dan Sheehan, 17–Ellis Genge, 18–Tadhg Furlong, 19–Joe McCarthy, 20–Scott Cummings, 21–Jac Morgan, 22–Ben White, 23–Marcus Smith.
