You might be remembering a performance of The Little Mermaid by the Little Angel Marionette Theatre of London (possibly on Wednesday, June 27, 1984, at 7:00pm).
A search for "little mermaid puppet" (but without the quotation marks) within the year range 1980-1984 on the Lansing State Journal archive site returns a match from the Saturday, June 23, 1984 issue. The archive thumbnail gives information about a performance that would take place on Wednesday, presumably June 27. This thumbnail in conjunction with a second thumbnail dated two days earlier allows us to piece together the name of the troupe...
https://lansingstatejournal.newspapers.com/search/?query=little%20mermaid%20puppet&dr_year=1980-1984
Clicking through the thumbnail to reach the full scanned image of the original article requires a subscription (which I do not have) but the headline behind the subscription challenge indicates the performance was at Michigan State University, as you had guessed.
The Wikipedia article regarding the Little Angel Theatre indicates it was
opened on 24 November 1961, by founders John and Lyndie Wright
and that it was
an internationally recognised theatre with productions touring throughout the UK and across the globe
The British Pathé channel on YouTube contains a short video with some coverage of the theatre in 1964. In the background throughout the first minute of the video, a few greenish marionettes can be seen that might be mermaids, and from 1m01s to 1m04s, a sign for The Little Mermaid show is displayed...
Whether or not they used the same puppets while touring overseas 20 years later, I could not determine. I was unable to find any related video from the 1980s.
The Little Angel Theatre is still active. Some additional information and history about them can be found at their website and their YouTube channel...
https://www.littleangeltheatre.com/
https://www.youtube.com/@TheLittleAngelTheatre