Can I say "She can distinguish her baby's cry from others'?

Yours is an example of noun ellipsis.

She can distinguish her baby's cry from others' cries. -->
She can distinguish her baby's cry from others' [ ].

However, I don't think that's what you mean to say. As constructed, your sentence could be comparing her baby's cry to, for example, the cries of elephants or doves.

I think you mean this:

She can distinguish her baby's cry from other babies' cries. -->
She can distinguish her baby's cry from other babies' [ ].

Your best bet is to rewrite without a possessive apostrophe:

She can distinguish her baby's cry from those of other babies.