Rooney was ruled out for at least a week with a hamstring injury ahead of Saturday's 1-1 draw at Stoke. Strike partner Javier Hernandez will also miss Tuesday's match after limping off early in the match that ended United's perfect start to its Premier League title defense.
While the draw at Stoke was United's first domestic slip this season, the team had already dropped points in the Champions League when it was held to a 1-1 draw at Benfica in its Group C opener.
United manager Alex Ferguson was already planning to rotate his squad against Basel at Old Trafford, but the injuries to Rooney and Hernandez will force him into an unexpected change up front.
While both Michael Owen and Danny Welbeck are in contention, Dimitar Berbatov could get a rare start on Tuesday leading the attack.
''He is one of our squad members,'' Ferguson said of Berbatov. ''It's an exhausting season unless you use your squad.''
United also has injury problems in defense, with Jonny Evans ruled out with an ankle problem and Chris Smalling sidelined with a groin injury. Nemanja Vidic has yet to start training after sustaining a calf injury last month.
Basel, which will be without striker Xherdan Shaqiri due to suspension, has a two-point lead over United and Benfica in Group C after beating Romanian champion Otelul Galati.
''I think we got a positive result against Benfica,'' Ferguson said. ''Hopefully, we can strengthen our position. Basel are a decent side though.''
Ferguson is hoping a victory over Basel is followed by back-to-back wins over Otelul Galati so he can rest players for the final Group C matches ahead of the packed December fixture list.
''If we win our next three games, we can utilize the squad,'' Ferguson said. ''It would definitely help and we've done that over the years. It's sometimes backfired - I played a fresh team over in Fenerbahce and they beat us 3-0. Although I want to make changes, I don't want an embarrassment. So changes have got to be made with a mind of still winning the game.''
United's experience in the European Cup could be key. The club has won the title three times, and reached the final in three of the last four seasons.
''We've built up experience playing in Europe, especially the team we have now,'' United midfielder Darren Fletcher said. ''A lot of us have been playing together for four or five years in Europe.
''We have found a way and a style of playing. We know how important it is to keep the ball. It is different to the Premier League - you give the ball away in Europe and foreign teams can keep it for long periods. We have learnt to adapt.''
Fletcher is already wary of the looming matches against Otelul Galati.
''You've got to be cautious about unknown quantities,'' he said. ''Some people expect you to just walk over teams like that and win comfortably. It's never as easy as that though.''
Benfica will find out for itself on Tuesday when it becomes Otelul Galati's first-ever Champions League opponent in Bucharest.
Away matches have proved tough for Benfica, which lost all three group matches on the road last season and hasn't won outside Lisbon in the tournament since the 2007-08 season.
But Benfica is unbeaten on four previous visits to the Romanian capital, last beating Dinamo Bucharest in the 2006-07 campaign.