The veteran centre-back sustained a groin injury during Sunday's league defeat to Celtic and has been forced to concede defeat in his battle to face the Italians.
With Weir ruled out, Carlos Cuellar is expected to be partnered in central defence by Christian Dailly.
Weir, 37, was in fine form against Fiorentina in the goalless first leg of the semi-final at Ibrox last Thursday, however Rangers must cope without the Scotland international for the return game.
Manager Walter Smith told the Evening Times: "Davie won't make Thursday night, which is a blow considering how important a player he is for us."
Smith is not ruling Weir out of Sunday's Clydesdale Bank Premier League clash with Hibernian.