Davidson, Watford midfielder Don Cowie, Blackpool left-back Stephen Crainey and Everton goalkeeper Iain Turner have been added to the squad following last month's victory over Northern Ireland.
Scotland face Brazil at the Emirates Stadium on March 27.
Stepping up: Davidson is in the Scotland squad to face five-time world champions Brazil in London
All four of the additions have been in squads before the Dublin friendly win, with Turner and Davidson joined by Blackburn defender Grant Hanley as the only uncapped players in the 24-man squad.
Captain Darren Fletcher is absent after missing Manchester United's most recent games through illness.
Scotland squad to face Brazil
Goalkeepers: A McGregor (Rangers), C Gordon (Sunderland), I Turner (Everton)
Defenders: C Berra (Wolves),P Bardsley (Sunderland),G Caldwell (Wigan), S Crainey (Blackpool), G Hanley (Blackburn), A Hutton (Tottenham), S Whittaker (Rangers), D Wilson (Liverpool), M Wilson (Celtic)
Midfielders: C Adam (Blackpool), B Bannan (Aston Villa), S Brown (Celtic), K Commons (Celtic), D Cowie (Watford), M Davidson (St Johnstone), J McArthur (Wigan), J Morrison (West Brom), R Snodgrass (Leeds),
Strikers: C Maguire (Aberdeen), K Miller (Bursaspor), S Naismith (Rangers)
The other three players to drop out of the squad originally named for the Dublin friendly win - West Bromwich midfielder Graham Dorrans, Rangers midfielder Lee McCulloch and Kilmarnock goalkeeper Cammy Bell - have all been injured.
Wigan midfielder James McArthur and Leeds winger Robert Snodgrass retain their places after playing in the 3-0 victory over Northern Ireland following late call-ups.
Rangers midfielder Steven Naismith also retains his place after recovering from a hamstring injury.
Wolves striker Steven Fletcher remains out of the picture after asking not to be considered for the Northern Ireland game.
Levein said: 'There are 24 players in this squad and it's fairly obvious not all are going to play.
'Some of the younger ones are here for experience. I feel this is a game that has such excitement, that it would be great for some of the younger players to come along and experience the occasion.
'Murray is one of those. I'm not saying Murray won't take part in the game but he is more along to gain experience.'
Levein, whose squad will prepare for the friendly with a five-day training camp in La Manga, Spain, added: 'He has a match on the Tuesday evening, the replay of the cup tie (against Brechin), so he will fly out to join us on the Wednesday.'
Levein has been trying to persuade Wigan midfielder James McCarthy to switch allegiance to his native country, but the former Hamilton player has been named in the Republic of Ireland squad for a Euro 2012 qualifier against Macedonia.
McCarthy, who qualifies for the Irish squad through his grandfather, has only played one friendly for the full team, against Brazil, so could still switch unless he plays a competitive game.
Levein said: 'James isn't in this squad. At this minute of time he hasn't played a competitive match for Ireland, if he does play a competitive international for Ireland, that will be it.
'I don't want to sit down at this particular juncture and talk about James McCarthy.'
Winning ways: Kenny Miller (2nd right) celebrates his goal in the 3-0 victory over Northern Ireland last month
Scotland 3 Northern Ireland 0: Captain Miller inspires Dublin strollCrash course: Celtic and SFA in fresh battle over Neil LennonRangers lodge appeal against McCoist's two-game touchline ban
Explore more:People: Craig Levein, Steven Fletcher, Darren Fletcher, James McCarthy Places: Leeds, Liverpool, Aberdeen, Dublin, Scotland, Northern Ireland, Brazil, Republic of Ireland, Ireland, Spain, Macedonia