Meanwhile Hull goalkeeper Allan McGregor and Derby striker Chris Martin were both restored to the squad, with Celtic forward Leigh Griffiths retaining his place.
Armstrong has impressed Strachan with his performances for Scottish champions Celtic.
"Itâs about dealing with the situation, dealing with the big-game mentality, dealing with the press that comes along and dealing with the crowds," said former Scotland midfielder Strachan.
"Thatâs something that the boys at Celtic have to deal with all the time, and Stuart, as far as I can see, is dealing with that well," added Strachan, himself a former Celtic manager.
Scotland are away to Georgia on September 4, three days before they face world champions Germany at Glasgow's Hampden Park.
All the teams in Group D have now played six matches.
Scotland are third with 11 points, three points behind leaders Poland and two adrift of Germany.
Scotland squad announced Monday for the Group D Euro 2016 qualifiers away to Georgia on September 4 and at home to Germany on September 7:
Goalkeepers: Craig Gordon (Celtic), David Marshall (Cardiff City/WAL), Allan McGregor (Hull City/ENG)
Defenders: Cristophe Berra (Ipswich Town/ENG), Craig Forsyth (Derby County/ENG), Gordon Greer (Brighton & Hove Albion/ENG), Grant Hanley (Blackburn Rovers/ENG), Alan Hutton (Aston Villa/ENG), Russell Martin (Norwich City/ENG), Charlie Mulgrew (Celtic), Andrew Robertson (Hull City/ENG), Steven Whittaker (Norwich City/ENG)
Midfielders: Ikechi Anya (Watford/ENG), Stuart Armstrong (Celtic), Scott Brown (Celtic), Darren Fletcher (West Bromwich Albion/ENG), James Forrest (Celtic), Shaun Maloney (Chicago Fire/USA), James Morrison (West Bromwich Albion/ENG), James McArthur (Crystal Palace/ENG), Matt Ritchie (Bournemouth/ENG), Johnny Russell (Derby County/ENG).
Forwards: Steven Fletcher (Sunderland/ENG), Leigh Griffiths (Celtic), Chris Martin (Derby County/ENG), Steven Naismith (Everton/ENG)