Bastareaud was one of his side's standout performers when they comfortably saw off Aviva Premiership leaders Harlequins in the last eight as he produced the kind of hugely powerful display that made him a star attraction during his time with semi-final opponents Stade.
The 23-year-old told reporters after that 37-8 thrashing of Quins that he loves playing in European competition but he will now have to wait a little longer than his team-mates to do so again.
Bastareaud damaged his hand in the disappointing domestic defeat Agen last weekend and scans have since shown he fractured a bone in his forefinger.
The French international centre is expected to spend a month on the sidelines and will therefore miss the Top 14 clashes with Castres, Stade Francais and Toulouse, as well as the Amlin semi at the Stade Felix Mayol.
Bastareaud now faces a race against time to be fit for the Amlin Challenge Cup Final if Toulon see of Stade, with the final taking place at the Twickenham Stoop on Friday, May 18.