Quinlan led Ireland to a 30-13 victory in the inaugural AIB Club International against Scotland last year, and a 20-17 defeat of England Counties at Donnybrook last month.
The side for Friday's game shows two changes from the one that started against England Counties.
Quinlan's place at number 8 goes to Cork Constitution skipper Frank Cogan, who moves up from the replacements bench, with Oisin Hennessy of Dungannon coming into the squad.
Dublin University hooker Matthew Crockett, who touched down against England Counties, is also unavailable due to injury so Kevin Corrigan of Lansdowne will start, with Garryowen's Damien Varley included in the matchday 22.
Team manager Mick Galwey said: "The loss of David and Matt is unfortunate, and disappointing particularly for the players themselves.
"But we have two excellent repacements in Frank Cogan and Kevin Corrigan and I would have no worries about their ability to perform, as both came on during the last game and they played very well."
Commenting on the win over England Counties, the Shannon boss added: "We were delighted with the team's performance last time out. They gelled together very quickly and really put it up to a physically bigger England side.
"But this game is an even bigger challenge and we will have to repeat that sort of performance if we want to be in with a chance of beating the Scots on Friday.
"Overall the experience has been fantastic for the management and the players, so we want to end the season on a high note."
IRELAND CLUB INTERNATIONAL TEAM AND REPLACEMENTS (v Scotland Club XV, Meggetland, Boroughmuir RFC, Friday, March 9, kick-of 7pm):
15 - Richard McCarter (Dungannon)
14 - Niall O'Brien (Clontarf)
13 - Kevin Hartigan (Garryowen)
12 - Glen Telford (Dungannon)
11 - Cronan Healy (Cork Constitution)
10 - Andrew Thompson (Shannon)
9 - Fiach O'Loughlin (Clontarf)
1 - Dan O'Connell (Galwegians)
2 - Kevin Corrigan (Lansdowne)
3 - Simon Shawe (Ballymena)
4 - Merle O'Connell (Cork Constitution)
5 - Alan Maher (Lansdowne)
6 - Peter Malone (Garryowen) (capt)
7 - Conor Hartigan (Buccaneers)
8 - Frank Cogan (Cork Constitution)
16 - Damien Varley (Garryowen)
17 - Stephen Nolan (Terenure College)
18 - Simon Crawford (Clontarf)
19 - Oisin Hennessy (Dungannon)
20 - Mark Bruce (Buccaneers)
21 - Barry Keeshan (Dolphin)
22 - Andrew Finn (Shannon)