The 39-year-old Sweden international, who missed this summer’s European Championship because of a knee injury, made a goalscoring return to action against Lazio over the weekend.
Ibrahimovic scored Milan’s second goal against Maurizio Sarri’s men at the San Siro on Sunday but felt the effects of an achilles tendon problem that will see him miss the pivotal trip to Merseyside.
Milan manager Stefano Pioli will have to choose between Ante Rebic and Olivier Giroud to lead his attack at Anfield.
Speaking in a news conference on Tuesday, 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."
AC Milan are playing in the Champions League for the first time since the 2013/2014 season.
The Rosonerri, who have won Europe’s premier club competition seven times, are also in the same group with Atletico Madrid and FC Porto.
