Spaniard Alonso had appeared to suffer a knee injury but was back on the pitch on Tuesday as Bayern continued their preparations for the home clash against the London club.
However, Bayern will be without their Germany central defender Jerome Boateng and French winger Franck Ribery, who both trained alone on Tuesday as they recover from injuries.
"(Alonso) is important for us. He can start from the beginning tomorrow (Wednesday)," Bayern coach Carlo Ancelotti told reporters on the eve of the game. "Ribery and Boateng cannot play tomorrow but everyone else is fit.
This is the fourth encounter between Bayern and Arsenal at this stage of the competition since 2005, with Bayern having advanced on the past three occasions.
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"We want to control the game," Ancelotti added. "Arsenal are good with counter-attacks they have quick players, we have thought about how to deal with this. But this a two-legged tie. It's 180 minutes."
Bayern, five-time European champions, lead the Bundesliga and are in the German Cup last eight as they chase a treble of titles despite lacking the dominance of past seasons.
"Sometimes we played well, sometimes we could have played better, but overall I am satisfied so far," Ancelotti, in his first season in charge, said.
"Tomorrow is a different game. It is two games (in the tie) but it will be important to play well, to defend well, have a good balance and be able to force our strategy."
Ancelotti said Arsenal, who are fourth in the Premier League, would be tough opponents but his side were aiming high.
"My team can hold their own against any team in this competition until the final. We have to focus on Arsenal but have to use our experience and quality to go as far as we can," the Italian said.
(Reporting by Karolos Grohmann; Editing by David Goodman and Ken Ferris)
