Can Nintendo 3DS Games Work on DSi? No — Hardware Incompatible

No. Nintendo 3DS games cannot play on a DSi.

Why

• Different hardware: 3DS has a more powerful CPU/GPU, dedicated 3D screen, and different architecture.
• Different OS: Incompatible system software.
• Different cartridges: 3DS cards have different pins/connectors; physically won't fit in DSi slot.

The systems are fundamentally incompatible. 3DS games only work on 3DS/2DS/New 3DS family.