Antonio was included on the same day he scored for the Hammers in their 3-1 loss away to Premier League leaders Manchester City.
The 26-year-old has adjusted well to life in the Premier League since joining the Hammers from Nottingham Forest a year ago.
He scored nine goals in 32 appearances for the London club last season, while his two most recent Hammers games have seen Antonio head in against both Bournemouth and City.
Jamie Vardy, a key figure in Leicester City's stunning Premier League title success last season, has already trodden the path from non-league to international football and the Foxes striker has also been included in Allardyce's first England squad.
Now the England manager is looking forward to seeing Antonio complete the same trip.
"This is another lad with a great journey -- it's a fantastic journey that he's been on, from non-league to now an international call-up. He scored nine goals in his first season and he's a terrific athlete, a good crosser and a goal-scorer," Allardyce said.
- 'Overwhelmed' -
=================
Meanwhile an emotional Antonio told West Ham's website: "I'm overwhelmed. It's just one of those things that I've always dreamt of playing for England as a kid, so now for it to happen after I've worked my way from non-league to where I am now, I am just so happy."
Antonio added: "I turned down an approach from Jamaica in March and for this to happen so quickly, I'm buzzing!
losing his first-team place at City under new manager Pep Guardiola while, equally unsurprisingly, Allardyce opted against recalling John Terry, the retired former England captain, after indicating he could contact the Chelsea centre-half.
However, there were recalls for Danny Drinkwater, a midfielder with English champions Leicester City, defenders Phil Jagielka (Everton) and Luke Shaw (Manchester United), as well as Arsenal's Theo Walcott after they all failed to make it into former England manager Roy Hodgson's squad in France.
Allardyce has yet to announce his England captain, although Manchester United's Wayne Rooney, who skippered the side at Euro 2016, was included in Sunday's squad as a midfielder.
England squad to play Slovakia in a 2018 World Cup Group F qualifier in Trnava on Sunday, September 4 (1600 GMT kick-off):
Goalkeepers: Fraser Forster (Southampton), Joe Hart (Manchester City), Tom Heaton (Burnley)
Defenders: Gary Cahill (Chelsea), Nathaniel Clyne (Liverpool), Phil Jagielka (Everton), Danny Rose (Tottenham Hotspur), Luke Shaw (Manchester United), Chris Smalling (Manchester United), John Stones (Manchester City), Kyle Walker (Tottenham Hotspur)
Midfielders: Dele Alli (Tottenham Hotspur), Michail Antonio (West Ham United), Eric Dier (Tottenham Hotspur), Danny Drinkwater (Leicester City), Jordan Henderson (Liverpool), Adam Lallana (Liverpool), Wayne Rooney (Manchester United), Raheem Sterling (Manchester City), Theo Walcott (Arsenal)
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