If you aren't using fetchBusinesses method anywhere apart from the effect, you could simply move it into the effect and avoid the warning

useEffect(() => {
    const fetchBusinesses = () => {
       return fetch("theURL", {method: "GET"}
    )
      .then(res => normalizeResponseErrors(res))
      .then(res => {
        return res.json();
      })
      .then(rcvdBusinesses => {
        // some stuff
      })
      .catch(err => {
        // some error handling
      });
  };
  fetchBusinesses();
}, []);

If however you are using fetchBusinesses outside of render, you must note two things

1. Is there any issue with you not passing fetchBusinesses as a method when it's used during mount with its enclosing closure?
2. Does your method depend on some variables which it receives from its enclosing closure? This is not the case for you.
3. On every render, fetchBusinesses will be re-created and hence passing it to useEffect will cause issues. So first you must memoize fetchBusinesses if you were to pass it to the dependency array.

To sum it up I would say that if you are using fetchBusinesses outside of useEffect you can disable the rule using // eslint-disable-next-line react-hooks/exhaustive-deps otherwise you can move the method inside of useEffect

To disable the rule you would write it like

useEffect(() => {
   // other code
   ...

   // eslint-disable-next-line react-hooks/exhaustive-deps
}, []) 

There are very good options for state management librariess if you are creating a new app or have enough flexibility. Check out Recoil.

Just for completeness:

1. (Stopped working) Use function as useEffect callback

useEffect(fetchBusinesses, [])

2. Declare function inside useEffect()

useEffect(() => {
  function fetchBusinesses() {
    ...
  }
  fetchBusinesses()
}, [])

3. Memoize with useCallback()

In this case, if you have dependencies in your function, you will have to include them in the useCallback dependencies array and this will trigger the useEffect again if the function's params change. Besides, it is a lot of boilerplate... So just pass the function directly to useEffect as in 1. useEffect(fetchBusinesses, []).

const fetchBusinesses = useCallback(() => {
  ...
}, [])
useEffect(() => {
  fetchBusinesses()
}, [fetchBusinesses])

4. Function's default argument

As suggested by Behnam Azimi

It's not best practice, but it could be useful in some cases.

useEffect((fetchBusinesses = fetchBusinesses) => {
   fetchBusinesses();
}, []);

5. Create a custom hook

Create a custom hook and call it when you need to run function only once. It may be cleaner. You can also return a callback to reset re-run the "initialization" when need.

// customHooks.js
const useInit = (callback, ...args) => {
  const [mounted, setMounted] = useState(false)
  
  const resetInit = () => setMounted(false)

  useEffect(() => {
     if(!mounted) {
        setMounted(true);
        callback(...args);
     }
  },[mounted, callback]);

  return [resetInit]
}

// Component.js
return ({ fetchBusiness, arg1, arg2, requiresRefetch }) => {
  const [resetInit] = useInit(fetchBusiness, arg1, arg2)

  useEffect(() => {
    resetInit()
  }, [requiresRefetch, resetInit]);

6. Disable eslint's warning

Disabling warnings should be your last resort, but when you do, better do it inline and explicitly, because future developers may be confused or create unexpected bugs without knowing linting is off

useEffect(() => {
  fetchBusinesses()
}, []) // eslint-disable-line react-hooks/exhaustive-deps

./src/components/BusinessesList.js
Line 51:  React Hook useEffect has a missing dependency: 'fetchBusinesses'.
Either include it or remove the dependency array  react-hooks/exhaustive-deps

It's not a JavaScript/React error, but an ESLint (eslint-plugin-react-hooks) warning.

It's telling you that the hook depends on function fetchBusinesses, so you should pass it as a dependency.

useEffect(() => {
  fetchBusinesses();
}, [fetchBusinesses]);

It could result in invoking the function on every render if the function is declared in a component like:

const Component = () => {
  /*...*/

  // New function declaration every render
  const fetchBusinesses = () => {
    fetch('/api/businesses/')
      .then(...)
  }

  useEffect(() => {
    fetchBusinesses();
  }, [fetchBusinesses]);

  /*...*/
}

because every time the function is redeclared with a new reference.

The correct way of doing this stuff is:

const Component = () => {
  /*...*/

  // Keep the function reference
  const fetchBusinesses = useCallback(() => {
    fetch('/api/businesses/')
      .then(...)
  }, [/* Additional dependencies */])

  useEffect(() => {
    fetchBusinesses();
  }, [fetchBusinesses]);

  /*...*/
}

Or just define the function in useEffect.

More: [ESLint] Feedback for 'exhaustive-deps' lint rule #14920