It is the second month in succession that Dyche, whose side lead Leicester by one point at the top of the table, has won the award.
A perfect October for Burnley saw them win four games, conceding just one goal.
Sky Sports' Football League pundit Don Goodman said: "Sean fully deserves his second Sky Bet Manager of the Month award in succession.
"The 2-0 victory over QPR showed how far his side have come. They should now be considered serious title challengers."
Burnley striker Ings scoops the player gong after having a month to remember. He made his England Under-21 debut - and got both goals in the 2-0 win against top-of-the-table rivals Queens Park Rangers.
Dyche said: "Danny has a desire to learn and improve, and is making very good strides on his journey into developing into a fine young player.
"In my opinion, he is fully deserving of this award."
Coventry City's Steven Pressley has been named the Sky Bet League One Manager of the Month after he guided his team through another stellar month, collecting 13 points from a possible 15.
Milton Keynes Dons striker Patrick Bamford picked up the player award for League One after helping himself to four goals in the month, including a brace at Gillingham. Another goal at Leyton Orient followed before netting the late winner in a 3-2 win against Rotherham United.
Hartlepool United's Colin Cooper lands the Sky Bet League Two Manager of the Month accolade after steering his side to four wins from five matches with an 11-3 goal tally.
Capping off an awards double for Hartlepool, striker Luke James is named Player of the Month after scoring three goals, including a deft lob that thrilled Pools fans in the 3-0 win at Exeter.
James bagged the winner with the only goal of the game against Plymouth Argyle, and also netted in the 3-1 win against AFC Wimbledon.