It shouldn't, I think. Since your target device is running at 1.1 volts, the maximum voltage it should see is the 1.1 volts from the pullup. Your target may have higher voltage input and output tolerance, but you haven't specified what it is.
Coming back the other way, the question would be if the I2C input can read 1.1 volts as a logic 1. That you can find out in the processor's voltage range definitions.
I typically run at 3.3 volts for the MCU, and 5 volts for board to board communications. Some modules I use are 5.0 volts only. I picked 5 volts because it's both common, and running 5 volt I2C should give me a higher noise margin.
To do the translation, I use a PCA9517 (relatively inexpensive SO-8 surface mount package). It has two separate VCC pins, and will translate easily from one supply voltage to another, or the same, in which case it provides buffering and offloads line capacitance.
I checked the specs, and the chip is designed to go from as low as 0.8 volts on the A side, to 2.5 volts+ on the B side. So it would allow you to go from your MCU to 3.3 volts, but because you have to use the chip in an A->B hookup (B <-> B not allowed), and the limitation of the B side is 2.5 volts. This doesn't work for you.
However, that doesn't mean that there aren't some of the PCA95xx chips that won't work, but it is an idea.
Because I use 3.3 volts to 5, then 5 to 3.3, the voltage levels match. I drive the B side with the processor (2.7 to 5.0 volts VCC), and then run the A side (5.0 volts) to all the other A sides. B can't be paralleled, but A can be. Due to the voltages you use, it won't work for you.
Look at the NVT2002DP, which is available in a TSSOP-8 (can be hand soldered) package. It may just be what you need if you decide to go that way. I think you have to drive it B (processor) to A (1.1 volt device), because VCCA has to be less than VCCB. I can do that with the PCA9517.
Good luck, though.
