He becomes only the third bowler in T20 International history to achieve the feat after Afghanistan's Rashid Khan and Lasith Malinga of Sri Lanka.
The Johannesburg-born Campher is also the second player with a hat-trick in the men's T20 World Cup after Australia fast bowler Brett Lee, who achieved the feat against Bangladesh in the inaugural edition in 2007.
Campher, 22, had a T20 best of 3-19 from his previous four matches since making his debut earlier this year against Zimbabwe in Dublin.
He switched ends in the match on Monday and got instant success after Ireland reviewed a caught behind for Ackermann with the ultra edge technology showing a spike when the ball passed the batsman's gloves.
Technology helped Campher once again on the hat-trick ball when Edwards was given not out by the on-field official but replays suggested the ball would have hit the leg stump.