Quins boss Tabai Matson revealed ahead of Friday’s Gallagher Premiership clash at Bath – which Quins won 19-13 – that Smith would be sidelined for at least a month due to an ankle injury suffered during England’s Autumn Nations Series defeat against South Africa last weekend.
That will rule him out of facing the Sharks in Durban, followed by a home appointment with French heavyweights Racing 92, then a Premiership encounter against Bristol at Twickenham and a trip to Northampton.
“We know he is definitely out for a month and then next week we will get a bit more clarity around what those timeframes are like,” Matson said.
“It’s disappointing for him, but he is quite a resilient lad and he hasn’t had many injuries, touch wood.”
Quins made it four successive Premiership wins on the back of tries by skipper Alex Dombrandt, centre Oscar Beard and full-back Nick David at the Recreation Ground.
And they moved just two points behind second-placed Sale Sharks as a result.
“We didn’t click in the first half, and we managed to get the benefit of some penalties,” Matson added.
“At the end of 80 minutes, considering the amount of mauls and players we had in the bin, that is a courageous effort. And ultimately, pretty lucky.
“As we roll into Europe, we knew it was important to get a gritty win. People dug in tonight.
“We take a squad of 30 (to South Africa), flying Sunday evening. It’s exciting.
“But we have really been trying to focus on this Bath game because it’s so important in the scheme of the season.”
Quins finished the game with 13 players after flanker Jack Kenningham and replacement hooker George Head received yellow cards.
A try count of 3-1 in Quins’ favour told its own story, though, and Bath could not get quite close enough.
Fly-half Tommy Allan kicked two conversions as Quins triumphed, while wing Will Butt scored a second-half try for Bath, Orlando Bailey and Piers Francis each landed a penalty, and Bailey a conversion.
Given their set-piece dominance, Quins should arguably have posted a more comfortable triumph, yet four points on the road against a Bath team bolstered by a number of recent new arrivals proved an impressive night’s work.
Bath head of rugby Johann van Graan said: “We had opportunities to win it.
“We were twice over their try line, and you couldn’t see a grounding of the ball. We created enough to win, but we didn’t, and that is disappointing.
“We have got to look at the technical detail of why we couldn’t get the ball down on the floor.
“But we were certainly tough to beat tonight, and we mixed it with one of the better sides in the Premiership.”
Additional reporting from PA