The injury-prone skipper, capped 21 times for Wales, has broken down with a recurrence of an old knee problem and has been ruled out for at least three weeks.
The Scarlets, twice losing Heineken Cup semi-finalists, will also be without Wales' World Cup wing Mark Jones for next Friday's clash as he undergoes knee reconstruction.
However Stephen Jones, Robin McBryde and Simon Easterby have all reported back for duty from the Six Nations Championship for tonight's Celtic League game against The Borders.
"It is unfortunate for Leigh who has a huge influence on the team with his experience but we feel confident in the rest of the guys that they can deal with this," said Scarlets coach Nigel Davies.
"It will be difficult because so many international players are coming back, the first time together is always pressurised.
"But it is vital that we get a result for our bid for the Celtic League title and we also need a good performance as a platform to go into the Biarritz game."
The Heineken Cup game, at Stradey Park, is already a 10,800 sell-out.