Use MenuItem.

class IconInSelect extends Component {
  ...
  render() {
    return (
      <Select>
        <MenuItem value="">
          <ListItemIcon>
            <InboxIcon />
          </ListItemIcon>
          <ListItemText primary="Inbox" />
        </MenuItem>
        <MenuItem value={10}>Ten</MenuItem>
        <MenuItem value={20}>Twenty</MenuItem>
        <MenuItem value={30}>Thirty</MenuItem>
      </Select>
    );
  }
}