React.version
is what you are looking for.
It is undocumented though (as far as I know) so it may not be a stable feature (i.e. though unlikely, it may disappear or change in future releases).
Example with React
imported as a script
const REACT_VERSION = React.version;
ReactDOM.render(
<div>React version: {REACT_VERSION}</div>,
document.getElementById('root')
);
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.1.0/react-dom.min.js"></script>
<div id="root"></div>
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