Jonas Eidevall's side were already assured of a place in the knockout stages, but ran riot nevertheless at Wefox Arena to ensure they would be seeded in the last eight.
Along with Maanum's treble, Caitlin Foord and Stina Blackstenius both scored a brace, while further strikes from Kim Little and Mana Iwabuchi completed the scoring.
"We scored some really good goals, and I'm happy to have got my hat-trick," Maanum told UEFA.com. "It's easier when you're surrounded by really good players. This is a nice early Christmas present, for sure!"
Arsenal were joined in the quarter-finals by Lyon, who are through to the last eight for the 14th time in 16 seasons after snatching second place in Group C with a goalless draw against Juventus.
Elsewhere, Barcelona ensured they advanced to the knockout stages as Group D winners following a thumping 6-0 victory over Rosengard.
Though already guaranteed progression beyond the group phase, Barca were in no forgiving mood as Asisat Oshoala scored twice with Mapi Leon, Fridolina Rolfo, Marta Torrejon and Irene Paredes also on target.
That took their goal tally to 29 - the highest in any Women's Champions League group stage - and meant Bayern Munich had to settle for second place despite Klara Buhl's double in a 2-0 win over Benfica.
The 2021-22 runners-up Barcelona will take on Roma in the last eight, while Paris Saint-Germain play Wolfsburg and Bayern Munich come up against Arsenal.
The first legs are scheduled for March 21 and 22, with the return fixtures a week later.
The semi-final draw was also made on Friday, with the winners of PSG and Wolfsburg set to face the winners of Bayern and Arsenal, while the winners of Lyon and Chelsea will go up against the winners of Barca and Roma.
Eindhoven will host the final on June 3.
Trailing to a Lea Schuller header from last week's first leg, Frida Maanum fired in a sensational 20-yard effort to level up the tie within 20 minutes of Wednesday's return game.
Stina Blackstenius powered in a header six minutes later to give Arsenal the lead in the tie for the first time in front of the 21,307 watching spectators in north London.
Jonas Eidevall's side missed chances to kill off the tie, but they saw out the victory to set up a meeting with the winners of Thursday's tie between Paris Saint-Germain and Wolfsburg.
Barcelona earlier booked their spot in the semi-finals, where either Chelsea or Lyon await, with a commanding 5-1 win over Roma at Camp Nou sealing a 6-1 aggregate victory.
Two-goal Fridolina Rolfo scored either side of Maria Leon's curler to put Barca, who finished runners-up to Lyon last season, out of sight before half-time.
Asisat Oshoala tapped in a fourth a minute after the restart and Patricia Guijarro headed in from a corner to complete the rout.
Competition debutants Roma registered a couple of attempts on target in the remaining 40 minutes, but it was plain sailing for Barca in their quest for a second European crown.
Gunners defender Frida Maanum put through her own net on the stroke of half-time to hand the reigning champions victory at the Emirates Stadium, leaving both sides on 10 points in Group C.
Jonas Eidevall's team knew they would qualify with anything less than a four-goal loss after establishing a head-to-head advantage by hammering Lyon 5-1 away from home in October.
However, the sight of a distressed Miedema leaving the field on a stretcher after appearing to catch her studs in the turf will provide cause for concern.
Miedema – the Champions League's top goalscorer in the 2016-17 and 2019-20 campaigns – has hit the net twice in the competition this season.
In Group C's other fixture, a four-goal haul from Cristiana Girelli helped Juventus profit from Irina Pando's red card in a 5-0 win over Zurich, teeing up a winner-take-all meeting with Lyon next week.
Meanwhile, Barcelona and Bayern Munich both ensured qualification from Group D, with the Spanish champions doing so in emphatic fashion with a 6-2 rout of Benfica.
Bayern joined them in racking up the goals with a 4-0 win at Rosengard, as Georgia Stanway joined Tainara, Sydney Lohmann and Julia Landenberger on the scoresheet.
