Same issue haunted my team for a while, and there's very little useful information about it on the web. We spent a lot of time troubleshooting the issue - and FINALLY found solution that solved it (at least - for our team)!
We found that Django sets "charset" option to "utf8" for database connections by default. During troubleshooting we used two separate database connection objects: one created for us by Django, and another - created manually using direct _mysql.connect() command. When we executed same exact query using both connection objects - the one created by Django resulted in "django.db.utils.OperationalError: (2027, 'Malformed packet')" (which is exactly what we were getting in our API), but the second connection (manual) - worked without any issues. Further comparison of the two connection objects (we actually had to use Python debugger "pdb" and set breakpoint within django.db.backends.mysql.base.py for that) - revealed that Django creates connection by passing "charset":"utf8", while manual _mysql connection - uses "latin1". As soon as we added "charset":"latin1" to DATABASES["default"]["OPTIONS"] within our settings.py - this error disappeared.
To summarize, solution (for us) was to explicitly set "charset":"latin1" within "OPTIONS" config section of DATABASES configuration - for every database alias. I can not say for sure that this will work for everyone who experiences this error - but it certainly works for us.
In general, any MySQL connection that uses "utf8" charset would perform the same way (generate this error); replacing that with "latin1" should solve it.