Germany forward Schueller scored the only goal of the game six minutes before half-time at the Allianz Arena, rising at the back post to head in a hanging cross from the right by Maximiliane Rall.
Arsenal, though, will feel they should have come away with at least a draw to take back for the second leg in London next week, with Caitlin Foord hitting the woodwork early in the second half.
Japan's Saki Kumagai then made a superb goal-line clearance to deny Stina Blackstenius, and Schueller made a similar intervention to prevent Leah Williamson from equalising.
"It was an even game and could have ended 1-1," said Bayern coach Alexander Straus.
"Arsenal were pushing us in the second half and we were defending deeper than we wanted to, so credit to them for that."
Arsenal, whose 2007 victory remains the only time an English club has won the competition, are looking to avoid going out to German opposition in the quarter-finals for the second year running after losing to Wolfsburg at this stage last season.
"We need to make sure to take our chances next week, and I'm sure we'll do that," said Arsenal captain Kim Little.
The return leg will be played at the Emirates Stadium next Wednesday, before which Bayern must face Wolfsburg in a meeting of the top two in the German Bundesliga at the weekend.
Wolfsburg, who have reached five Champions League finals in the last decade, winning two, visit Paris Saint-Germain in the first leg of their quarter-final tie on Wednesday, when holders Lyon take on Chelsea.
Barcelona edged Roma 1-0 in the first leg of their Women's Champions League quarter-final tie on Tuesday.
Nineteen-year-old Salma Paralluelo curled in a strike from the edge of the area in the 34th minute for Barcelona at the Stadio Olimpico. That proved enough to take a lead back to Catalonia for next week's return leg.
Barcelona found themselves up against it in the closing stages, with captain Sandro Panos making fine late saves to deny Manuela Giugliano and Valentina Giacinti in front of a crowd of more than 39,000.
Barcelona will be favourites to advance to the last four as they seek to reach a third consecutive final. They won the title in 2021 and were runners-up to Lyon last season.
