Jackett takes the boss award after guiding newly-promoted Wanderers to third place in the early table, with four wins from their first five league games.
Addicks striker Vetokele lands the Player prize after averaging a goal a game in the Championship thus far since his summer switch from FC Copenhagen.
The judging panel is chaired by former Football League manager Dave Bassett, and also includes Sky Sports' Football League expert Don Goodman, Football League Chief Operating Officer Andy Williamson, League Managers' Association Director Olaf Dixon and Sky Bet Football Trading Manager Paul Lowery.
In Sky Bet League One, Darren Ferguson is named Sky Bet Manager of the Month with his Peterborough United side setting the early pace, while Barnsley's new Irish midfielder Conor Hourihane is the Player of the Month for August.
The Sky Bet League Two Manager of the Month Award goes to Morecambe manager Jim Bentley following the Shrimps' excellent start to the campaign, and AFC Wimbledon striker Matt Tubbs is the Player award winner.
Here, Sky Sports takes a more in-depth look at the award winners...
Championship Manager of the Month: Kenny Jackett (Wolves)
Jackett's Wolves picked up where they left off in May, with four wins from five and just two goals conceded.
Most impressively, they recorded 1-0 victories over Norwich, Fulham and Cardiff - the three clubs relegated from the Premier League.
Bassett said: "Wolves have enjoyed an excellent start to life back in the Sky Bet Championship after their promotion last season.
"Nottingham Forest also had an excellent start under Stuart Pearce but I have chosen Kenny as I think Wolves just shaded it, when you consider the quality of opposition they defeated in August."
Championship Player of the Month: Igor Vetokele (Charlton)
There were five goals in as many games for 22-year-old livewire Angola striker Vetokele, who offers Charlton a threat in behind defences.
His skill was exemplified by both a low 20-yarder and a mazy run for his two goals at Brighton.
Charlton manager Bob Peeters, who accepted the award on Vetokele's behalf said: "Igor has made an impact and shown what a player he can be. But the whole team deserves recognition because we have all worked well together to help Igor get the goals."
Don Goodman said: "Vetokele has taken the Championship by storm after arriving from FC Copenhagen. He is going to be difficult to stop."
League One Manager of the Month: Darren Ferguson (Peterborough)
Ferguson masterminded a flying start, with four wins out of five to make light of the departure of last season’s leading scorer Britt Assombalonga.
He fitted new-boy Kyle Vassell seamlessly into the Posh attacking way to finish August at the head of the table.
Bassett said: "Darren's Peterborough side have continued where they left off last season by scoring goals in abundance whilst playing attractive football.
"Winning three matches away from home against high calibre teams indicates the Posh will once again be a team to watch this campaign."
League One Player of the Month: Conor Hourihane (Barnsley)
The 23-year-old Irishman served up a personal goal of the month competition with stunning efforts against Coventry, Gillingham and Yeovil.
Just as vital was his headed goal-line clearance which preserved the 1-1 draw at Huish Park.
Barnsley manager Danny Wilson said: "I am delighted with the impact Conor has had here. The award is thoroughly deserved. I am sure he will be looking for more!"
League Two Manager of the Month: Jim Bentley (Morecambe)
Bentley inspired the players around him to four straight wins to start the campaign.
The team spirit he engendered was shown in abundance in the 3-2 comeback win over Newport County.
Bassett said: "Bentley has masterminded a great start for Morecambe in Sky Bet League 2.
"Their four straight wins marked a great start to the new season for the Shrimps where they are amongst the early pace setters."
League Two Player of the Month: Matt Tubbs (AFC Wimbledon)
Tubbs' finishing ability is setting him apart in League Two. Four sharply-taken goals in five games, bearing his trademark combination of positioning and pace, have been pivotal to Wimbledon's comfortable start.
Dons manager Neal Ardley said: "This award is thoroughly deserved. Matt has been involved in six out of our seven league goals. I know - I do the stats!"
Goodman said: "Matt’s goal-scoring prowess has set him apart already. Four in five is a fantastic return."