Some obvious ones:
Phonetics, be it of spoken or signed language, is obviously constrained by the body of humans - both in the channels (aural, visual) employed and also in how they are employed.
Metaphors often make use of body parts. Spatial prepositions and adverbs are often derived from relevant body parts: front from face, forehead, nose, chest; back from back or butt; up from head… you get the picture. Basically every organ has been referred to as being the cause of emotions etc as well in metaphors.
Words for directions in particular are also somewhat based on human anatomy. We have lateral symmetry (left-right) but an alien could likely have some form of radial symmetry in their bodies, which would make the concepts of leftness and rightness very weird to them. Aquatic beings would also likely have a different concept of directions altogether, probably based more on the orientation of their own bodies than relative to the ground.
Those are the things that come to mind. However, much more importantly, the inner workings of language as a whole would likely be different from a human’s. There are some things in human language that you really wouldn’t assume to be necessary. Just to make two examples:
It seems pretty clear that humans take the raw audio input, break it into segments (phones) then further abstract those phones into phonemes, which are then in turn used to build more complex words. One could just as well imagine skipping the segmentation step and going directly from audio to meaning. There appears to be evidence however that some songbirds also employ what could be considered phonemes in their songs, so perhaps it is to be expected.
Another thing is in syntax: human language does not appear to allow circular dependencies, that is word¹ A modifying word B, which in turn modifies word A again. From my fairly limited understanding of syntax, human sentences can be structured in a tree structure. It seems plausible that an alien language might have more or less freedom, perhaps allowing cyclic graphs in their syntax… or in the other direction, only linear dependence. An example of an alien conlang playing around with this is Europan, which I personally consider one of the most interesting conlangs I’ve ever encountered.