Material UI Base Fiddle

HTML

<script src="https://unpkg.com/[email protected]/dist/react-with-addons.js"></script>
<script src="https://unpkg.com/[email protected]/dist/react-dom.js"></script>
<script src="https://rawgit.com/lechup/c5d51b8e474f7b5d48bafe3ef0f958b7/raw/0a2f0a5f96095f88f3e47fa78cb3daf023585698/MaterialUI.v.0.18.5.umd.min.js"></script>
<br /><br /><br /><br /><br /><br />
<p>Type anything and scroll to see bug</p>
<div id="container"></div>

CSS

.scrollWrapper {
  overflow: auto;
  height: 500px;
}

.scroll {
  height: 1000px;
}

Babel + JSX

const { MuiThemeProvider, AutoComplete } = MaterialUI;

 class AutoCompleteExample extends React.Component {
	constructor(props) {
    super(props);
    this.scrollWrapperElement = null;
  }
  state = {
		dataSource: []
  }
  
  handleUpdateInput = (value) => {
    this.setState({
      dataSource: [
        value,
        value + value,
        value + value + value,
      ],
    });
  };
  
  render() {
    return (
      <div className="scrollWrapper">
        <div ref={(scrollWrapperElement) => {this.scrollWrapperElement = scrollWrapperElement;}} className="scroll">
          <AutoComplete
            hintText="Type anything"
            dataSource={this.state.dataSource}
            onUpdateInput={this.handleUpdateInput}
            anchorEl={this.scrollWrapperElement}
          />
        </div>
      </div>
    );
  }
}

const App = () => (
  <MuiThemeProvider>
    <AutoCompleteExample />
  </MuiThemeProvider>
);

ReactDOM.render(
  <App />,
  document.getElementById('container')
);