Spain's taking issue with Katy's music vid for her new single "Lifetimes" ... which she filmed on the Balearic islands, and one scene where she's dancing and sitting on some sand dunes is reportedly catching the government's watchful eye.

The regional government's Department of the Environment is investigating, claiming the production company behind her music video was NOT authorized to film there ... according to multiple reports out of Spain.

The main issue here ... Katy's seemingly filming in the middle of protected dunes on the islet of S'Espalmador, an area Spain says has great ecological value.

In the music video, it looks like the dunes in question are roped off -- indicating a protected area -- and Katy's smack in the middle of it all ... presumably with a camera crew, production team and a ton of equipment in tow.

The Environmental Department says a preliminary investigation is underway to determine if there's a possible violation here.