Tuesday night's 3-1 win over Arsenal at the Emirates Stadium means Bayern have a handsome advantage ahead of the home leg on March 13.
After receiving his third booking in this season's competition, midfielder Schweinsteiger will be suspended when Arsenal visit the Allianz Arena.
That means the Germans will be without a star man, but goals from Toni Kroos, Thomas Muller and Mario Mandzukic have put Bayern in control of the tie.
Schweinsteiger appreciates that, but says there can be no slacking at this stage.
"We really got going well, especially in the first 30 minutes, when we let the ball and our opponents do the work," Schweinsteiger said.
"We were ruthless, especially in terms of taking our chances, but the third goal was vital too."
He said on Bayern's official website: "We mustn't underestimate Arsenal, they have some very good players, and we'll have to give it 100 per cent in the return. Arsenal aren't just dropping by as tourists. It's a good result, but it's not over yet."
For midfielder Kroos, there was disappointment that Bayern did not leave London with a clean sheet.
Kroos said: "We were outstanding for very long spells against a top European club.
"There was a phase just before and just after the break when Arsenal got at us, but you'll never entirely prevent that.
"They failed to create clear-cut chances, but it hurts to let in a goal, and it shouldn't be happening."
Champions League Winner 12/13 Win Outright: Bayern Munich 4/9
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