There are a couple instruments call “Money Market”
The ones called MMDA “Money Market Deposit Account”, offered by your FDIC-insured bank are insured.
Here’s excerpt from FDIC paper…
“Money Market Mutual Funds (MMMFs) are sometimes confused with money market deposit accounts (MMDAs). MMDAs are savings deposits that can be issued only by FDIC-insured banks and thrifts. Subject to FDIC coverage rules, deposits are insured up to $100,000. MMMFs are not FDIC-insured, and while it is extremely rare, investors can lose principal.”