There is no law or regulation that says that an institution can't buy an OTC stock.
That said, many institutions have internal bylaws that restrict the range of stocks they can buy. Some of those bylaws may be of the form "must be on Nasdaq or NYSE", but more likely they would be things like must have audited financials, must have a certain market cap, must have a given level of daily dollar volume, etc.
Institutions CAN buy otc stocks, but few otc stocks meet the criteria applied by most institutions to everything in their portfolio.