Fletcher picked up an injury in his side's Championship play-off semi.
Uncapped fellow forward Jamie Murphy, of Brighton, Hibernian's John McGinn and fellow midfielder Kenny McLean, of Aberdeen, also miss out.
Hearts goalkeeper Jack Hamilton is not needed after being named as cover.
Scotland host England in a World Cup Group F qualifier on 10 June.
Celtic left-back Kieran Tierney remains in the squad despite suffering a facial injury that forced him to be substituted in the first half of Saturday's 2-1 Scottish Cup final win over Aberdeen.
It means that six players remain from Brendan Rodgers' side who completed the Scottish domestic treble.
Fletcher, who forced his way back into the Wednesday starting line-up at the expense of Scotland colleague Jordan Rhodes, scored five goals in the last seven games of the season.
He helped his side into the Championship play-offs and, although they lost on penalties to Huddersfield Town in the semi-finals, the 30-year-old scored in the second leg.
McLean also earned praise for his performance in Aberdeen's defeat by Celtic at Hampden.
Murphy and McGinn both helped their clubs win promotion to their respective top flights.
Scotland go into the game at Hampden sitting fourth in Group F, two points behind second-top Slovakia, with England a further four points ahead.
Goalkeepers: Craig Gordon (Celtic), David Marshall (Hull City), Allan McGregor (Hull City)
Defenders: Ikechi Anya (Derby County), Christophe Berra (Ipswich Town), Stephen Kingsley (Swansea City), Russell Martin (Norwich City), Charlie Mulgrew (Blackburn Rovers), Mark Reynolds (Aberdeen), Andrew Robertson (Hull City), Kieran Tierney (Celtic)
Midfielders: Stuart Armstrong (Celtic), Barry Bannan (Sheffield Wednesday), Scott Brown (Celtic), Tom Cairney (Fulham), Darren Fletcher (West Bromwich Albion), Ryan Fraser (Bournemouth), James Forrest (Celtic), James McArthur (Crystal Palace), James Morrison (West Bromwich Albion), Robert Snodgrass (West Ham United)
Forwards: Leigh Griffiths (Celtic), Chris Martin (Derby County), Steven Naismith (Norwich City)
Sheffield Wednesday striker Steven Fletcher is one of five players out of the Scotland squad to face England after head coach Gordon Strachan slimmed down his original 29.