Christophers aggravated a pre-existing rib injury this week in training.
After last Sunday's 18-6 win over the Sharks, Bristol Shoguns go into the new year in eighth place in the Zurich Premiership after a decent run of results that includes 20 points from their last five league outings.
Commenting on the club's official website, Peter Thorburn said: "You look around the Premiership and the fixture list and there is not one easy game to be had. We had a difficult first few weeks to the season and we're not clear of bottom place yet.
"Saturday will be a tough game. Quins are strong at home and have beaten some very good sides at the Stoop. They'll also be on the rebound from last weekend's defeat at Bath and will want to start the year off well."
Bristol Shoguns: 15 Lee Best, 14 Brendon Daniel, 13 Andrew Higgins, 12 Daryl Gibson, 11 Phil Christophers, 10 Felipe Contepomi, 9 Agustin Pichot, 8 Ross Beattie, 7 Rhys Oakley, 6 Matt Salter, 5 Alex Brown, 4 Garath Archer (captain), 3 Julian White, 2 Paul Johnstone, 1 Andrew Sheridan.Replacements: 16 Darren Crompton, 17 Chris Rowland, 18 Chris Morgan, 19 Scott Morgan, 20 Peter Richards, 21 Matt Carrington, 22 Jamie Williams.
Kick-off: Saturday, 1500 GMT