Can I do an MS in biotechnology after a bachelors degree in chemical engineering?
This will probably to a high degree depend on the (exact) curriculum and prerequisites of your chosen bachelor and master.
Also note that I'm not from the US and judging from the terms you are using, it seems that you are, so everything I say is also a bit speculative.

In general biochemistry and to some degrees also biotechnology will have a lot of overlap with many aspects of chemistry (or at least organic chemistry). Depending of the focus of each program this might, make it possible to switch over from one to the other. One thing you will definitely not learn in any chemical mayor is molecular biology, which may well be a requirement for studying in any biotech related field later on.

If both your majors focus more on the technological aspect and less on the biological or chemical you should probably be fine. The equipments used in (modern) biology and chemistry is in many cases similar, though biotech involves more equipment specialised for the handling and analysis of cells. The underlying principles are still the same though.

In your case I would recommend you to check the requirements of different MS or grad schools, that you'd be interested in first, and the see if you can meet these with a chemical engineering mayor (and maybe/probably some added courses like molecular biology).