The 29-year-old made his long-awaited return following ankle surgery after last featuring for the Bundesliga leaders during their 1-0 Champions League victory over Viktoria Plzen in early November.
Bayern claimed a 2-0 victory over Arsenal in the first-leg last-16 clash at the Emirates Stadium and are on target to progress further unless Arsene Wenger's side can cause an upset in the return leg in two weeks' time.
Bayern would create history by defending their European crown and that is what Schweinsteiger has set his sights on, telling his club's official website: "I want to help Bayern retain the Champions League title.
"No other team has managed that and that's pure motivation for me."
The 4-0 win at Hannover on Sunday was the Germany midfielder's first start since for Pep Guardiola's team and he was delighted he suffered no adverse reaction following his comeback.
"It did me good to play from the start and not have any problems," added Schweinsteiger, who played for over 70 minutes before he was substituted.
"I've got to find my rhythm and I need time on the pitch to get fully fit again. I hope everything will go my way from this point."