The Lions have said that no decision has been made on whether O'Connell will leave or stay with the squad Down Under.
Lions forwards coach Graham Rowntree said: "Paul's a massive loss. He is such a big influence on the group and has been playing exceptionally well. But you have to get on with these things.
"I'd like him to stay on, but I'm not sure what he will do. You just have to roll with the punches when it comes to injuries."
It is a cruel blow for the 33-year-old lock who has had a key role in the tour to date, being a try-scoring captain against the Barbarians before featuring in the wins over the Queensland Reds and NSW Waratahs.
O'Connell was in talismanic form in the Lions pack as they emerged as 23-21 winners over Australia in last Saturday's opening match of the Test series.
The Limerick man, who captained the Lions to a third Test victory over South Africa in 2009, had continued his second row partnership with Wales' Alun Wyn Jones to very good effect.
Reacting to the news, O'Connell's Ireland colleague Sean O'Brien commented: "Paulie is obviously a massive loss. It's a decision for him to make if he wants to stay on. He's a big influence. Personally I'd like to see him stay on.
"The injuries aren't too big a problem. We have lads to cover in all positions and that shows the strength of the squad."
Either England's Geoff Parling or Richie Gray from Scotland will deputise for O'Connell when Warren Gatland's men clash with the Wallabies in Melbourne next Saturday.
Meanwhile, Dan Lydiate will now captain the Lions against the Melbourne Rebels in their final midweek game at AAMI Park on Tuesday.
Dragons flanker Lydiate will lead the team instead of Parling, who has been withdrawn from the starting line-up following O'Connell's tour-ending injury.
Ospreys second row Ian Evans will start against the Rebels in place of Parling. Ireland's Tom Court has been drafted onto the replacements bench for Mako Vunipola, who is being rested as cover for the second Test due to Alex Corbisiero's calf injury. Tom Croft comes on to the bench for Evans.
BRITISH & IRISH LIONS Team & Replacements (v Melbourne Rebels, 2013 British & Irish Lions Tour, AAMI Park, Melbourne, Tuesday, June 25, kick-off 7.40pm local time/10.40am Irish time):
15. Rob Kearney (Leinster/Ireland)
14. Sean Maitland (Glasgow Warriors/Scotland)
13. Manu Tuilagi (Leicester Tigers/England)
12. Brad Barritt (Saracens/England)
11. Simon Zebo (Munster/Ireland)
10. Owen Farrell (Saracens/England)
9. Conor Murray (Munster/Ireland)
1. Ryan Grant (Glasgow Warriors/Scotland)
2. Richard Hibbard (Ospreys/Wales)
3. Dan Cole (Leicester Tigers/England)
4. Richie Gray (Scotland))
5. Ian Evans (Ospreys/Wales)
6. Dan Lydiate (Newport Gwent Dragons/Wales) (capt)
7. Sean O'Brien (Leinster/Ireland)
8. Toby Faletau (Newport Gwent Dragons/Wales)
16. Rory Best (Ulster/Ireland)
17. Tom Court (Ulster/Ireland)
18. Matt Stevens (Saracens/England)
19. Tom Croft (Leicester Tigers/England)
20. Justin Tipuric (Ospreys/Wales)
21. Ben Youngs (Leicester Tigers/England)
22. Billy Twelvetrees (Gloucester/England)
23. Stuart Hogg (Glasgow Warriors/Scotland)