The 39-year-old former Manchester United striker made a goalscoring return for Milan as a substitute against Lazio on Monday (AEST), coming on to tap in the second goal in a 2-0 Serie A victory.
That followed a four-month knee injury lay-off, and the Swedish frontman has now reportedly suffered discomfort in an Achilles, forcing him out of plans for Thursday's (AEST) Anfield tussle.
That means coach Stefano Pioli will name Ante Rebic or former Arsenal and Chelsea striker Olivier Giroud as his attacking spearhead when he selects his side to face Jurgen Klopp's Reds.
Pioli stated Giroud would not be able to play a full 90 minutes, having returned from a spell on the sidelines after testing positive for COVID-19.
Speaking in a news conference on Wednesday (AEST), Pioli said: "Zlatan has had an inflammation; he gave it a go this morning but it's useless to take risks at this point of the season.
"I see AC Milan with Zlatan and I absolutely think we'll have him back soon. Absences are a part of football; I'll need to choose between Ante and Olivier but we have the cover."
Ibrahimovic has abundant Champions League experience, scoring 48 goals in the competition from 120 games, with nine of those coming for Milan between 2010 and 2012 in a previous spell with the Rossoneri.
The Swede has scored for more teams in the Champions League than any other player (six – Paris Saint-Germain, Milan, Ajax, Juventus, Inter Milan, Barcelona).
He arrived from LA Galaxy midway through the 2019-2020 season and helped Pioli take Milan into the Champions League for the first time in eight years with last term's second-placed finish in Serie A.
They last featured in the competition in the 2013-2014 campaign, a worrying drought for the club that have won the European Cup or Champions League on seven occasions.
"Our growth over the past year is clear for all to see," Pioli said. "Our experiences have helped us to grow and improve, and the beginning of this season has shown that this team knows how to play and how to approach games.
"The level is higher now; it's what we wanted and it's a chance for us to show that we can mix it with the best."
Milan has won just one of its last 13 games against English opponents in European competition (D4 L8), with that lone victory a 4-0 drubbing of Arsenal at San Siro in the Champions League in February 2012.
Pioli said: "Many of us have never played in the Champions League, but football is football. We know what to do and how to try and play against a really strong side.
"We've prepared really well for this game. There are no easy fixtures in this group; our opponents are all highly competitive and have been playing European football for a while. It's a chance for us to start writing our own history; we have a lot of belief in our own quality."