I am finishing a Ph.D. in psychology, but my goal is to find an industry job in biomedical engineering. Would an academic postdoc in biomedical engineering improve my prospects for an industry job in that field?
A PhD is a very high level qualification but going from psychology to biomedical engineering is quite a big change. So anybody who wants to hire somebody to do biomedical engineering would need some pretty strong arguments why they should hire you as a psychology phd. This applies to the professor looking for a postdoc the same way as in industry.
In comments you said you already have a postdoc offer. This seems to change things a lot because after the postdoc you can apply to biomedical engineering jobs and show you are qualified for them with the postdoc. Currently it seems very hard to judge your qualifications in that field.