Laudrup suffered an ankle injury during Sunday's 3-0 victory over Aberdeen at Pittodrie which took Rangers five points clear at the top.
The Danish international will join fellow foreigners Jorg Albertz and Joachim Bjorklund on the sidelines for the trip to France.
Paul Gascoigne, the England midfield player, is suspended again in the third instalment of his four-match Uefa ban for being sent off against Ajax in October.
Archie Knox, the Rangers assistant manager, said: "It is obviously a major blow to us for Wednesday given the rich vein of form which Brian has been in."
Laudrup scored the second goal at Pittodrie with his ninth of the season and Rangers will be desperate to have him fit to take on Hibernian at Ibrox on Saturday and Dundee United at Tannadice next Tuesday.
As well as Laudrup, Albertz, Bjorklund and Gascoigne, Rangers have other players ruled out including Stuart McCall, Gordon Durie and Alex Cleland.
Youngsters such as Greg Shields and Scott Wilson will both be included and skipper Richard Gough should be passed fit despite taking a knock on Sunday.
The travelling party will also include Trevor Steven and Alan McLaren. McLaren has not played a first-team game this season after knee surgery but is almost ready to return. Charlie Miller, Ian Ferguson and Derek McInnes are all in contention for midfield places.
The head of security at Rangers has warned that a serious accident is waiting to happen unless missile-throwing thugs are stopped.
Alistair Hood, who has more than 10 years experience of dealing with crowd behaviour at Ibrox, was speaking in the wake of the latest violent act by supporters at Pittodrie when Aberdeen supporters threw bottles at the Rangers club coach. Nobody was on board and no serious damage done to the bus. Aberdeen now studying video film to try to trace the culprits. The incident comes after an outbreak of coin-throwing at Stark's Park, Tynecastle and Celtic Park in recent matches.
"I am concerned that a serious injury will be sustained either inside or outside a football ground if missiles continue to be thrown," Hood said.
"It is senseless and needless but it is only a matter of time before someone is badly hurt if it carries on. People talk about closed circuit TV as a panacea for this but unless you have a camera trained on the culprit then there is very little you can do to trace the person.
"Clubs are doing what they can but if your back is turned and somebody throws something then there is very little you can do."
Hood insists he does not detect a rise in crime in the recent past compared to 10 or 15 years ago but added: "We have to keep being vigilant and we can't take the foot off the pedal. Like the police, football clubs rely on other supporters being willing to point out those who have done something wrong."
Hood has seen around 400 supporters at Ibrox for various offences and insists banning fans from their home stadium is a deterrent.
Aberdeen have said they will consider that a possible punishment if they can trace the fans involved in the incident.
David Johnston, the general manager at Pittodrie, said yesterday: "We are co-operating with the police on this and there has been no movement on it so far.
"We are trying to promote football yet a couple of mindless people do this. It shouldn't be forgotten that we had around 20,000 fans inside the ground and not one incident of note.
"Everybody was in their correct area and from a policing and stewarding point of view the match went off well."
Paolo di Canio, the Celtic player, will miss a two matches after Saturday's red card against Hearts. Di Canio is automatically suspended for tonight's night's rearranged Premier Division match against Dunfermline at East End Park. The Italian will also be banned when Celtic face Raith at Stark's Park on Saturday, 14 December.