The 38-year-old was arrested after fireworks were set off in a common stair in Dunsyre House North in the city's Wester Hailes on Tuesday evening.
Police also launched an investigation after a group of young people were spotted taking a quantity of fireworks from a vehicle that same night.
The pyrotechnics were then used during disorder and antisocial behaviour in Gracemount.
The 40-year-old man was arrested during efforts to trace the driver of the vehicle. He will appear in court on Tuesday.
Det Ch Insp George Calder said the force had been "unrelenting" in their pursuit of those responsible for disorder that had put communities "in a state of alarm" on Bonfire Night.
He said the three arrests were the first of many, adding: "You might think you have evaded arrest, because we’ve not yet come to your door, but we will be doing so imminently."