Good question. I don't recall a specific exclusion for IFR capability, but...

An LSA can be:

1. A purpose-built factory airplane certified under LSA rules
2. A homebuilt experimental which meets LSA rules
3. A standard category manufactured airplane which happens to meet LSA criteria.

In the case of #3, it could very well be certified for IFR from the factory.

In the case of 1 & 2, the limitation is that the airplane is certified under LSA, not standard airworthiness rules. Do the LSA certification rules make any provision or allowance for IFR certification? I don't think so, so now the question becomes...

EDIT: Information on the EAA website implies that there is nothing which forbids an LSA from being "certified" for IFR, but EAA does not know of any manufacturer which has done so yet. They imply that it might be in the works, although I imagine they might have liability concerns.