Yes, it is recommended to use a level shifter. According to the Breakout board hardware guide Intel® Edison Boards and Compute Modules — Intel® Edison Breakout Board Hardware Guide section 1 “The Intel® Edison Breakout Board is designed to expose the native 1.8 V I/O of the Intel® Edison module.” And according to your sensor datasheet VDD= 2.375V-3.46V.
There is a thread in the community Re: Suggestions for level shifters to use with mini breakout board of suggestions for level shifters for the mini breakout board where users list some of the level shifters they’ve used, give it a look.
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The MPU-6050 also supports different supply (VDD) and I/O interface (VLOGIC) voltages. If your board allows you to make separate connections to VDD (on pin 13) and VLOGIC (on pin 8), leave VDD on 3.3V and connect VLOGIC to 1.8V. Connect the pull-up resistors on SDA and SCL to 1.8V. The MPU-6050 will then speak I2C directly at 1.8V, eliminating the need for a discrete level shifter.
Quite a few sensor ICs support this kind of split-voltage operation, but not many off-the-shelf breakout boards make it easy to supply different voltages.