No. They are physically and electrically incompatible.
| Feature | PSP Memory Stick (Pro Duo) | Nintendo DSi (SD Card Slot) |
|---|---|---|
| Form Factor | 31.0 x 20.0 x 1.6 mm (Pro Duo) | SD / SDHC (32 x 24 x 2.1 mm) |
| Pinout / Protocol | Sony Serial / Parallel (Memory Stick) | SD Bus (SPI / 1-bit / 4-bit SD) |
| Voltage | 3.3V / 1.8V (Pro Duo) | 3.3V / 1.8V (SDHC) |
| Keying | Single notch (corner) | Two notches (asymmetric) |
The DSi only accepts standard SD (≤2GB) and SDHC (4GB–32GB) cards. It does not support Memory Stick, microSD (without adapter), or xD-Picture Card.
Solution: Buy an SD/SDHC card (Class 4 or 10 recommended) for DSi. For PSP, use Memory Stick Pro Duo (Mark 2 / Pro-HG for speed). Adapters (MS-to-SD) exist but are unreliable and not recommended for save data.