It needs to be DDR3 (for pin count and layout) but it does not need to be 1600 MHz, the system will configure the faster RAM to run at the slower RAM speed, for instance, if you buy a 1866 MHz stick, it will run at 1600 MHz. If you buy a 1333 MHz stick your current stick will step down to 1333 MHz to match.
For best performance, you should buy a 1600 MHz stick or faster with the same latencies or better.
Usually, from an economic perspective, the best choice is to go with the same ram you already have.