要使用 Material UI 设置必需的 Select 字段，您可以执行以下操作：

class SimpleSelect extends React.PureComponent {
  state = {
    selected: null,
    hasError: false
  }

  handleChange(value) {
    this.setState({ selected: value });
  }

  handleClick() {
    this.setState(state => ({ hasError: !state.selected }));
  }

  render() {
    const { classes } = this.props;
    const { selected, hasError } = this.state;

    return (
      <form className={classes.root} autoComplete="off">
        <FormControl className={classes.formControl} error={hasError}>
          <InputLabel htmlFor="name">
            Name
          </InputLabel>
          <Select
            name="name"
            value={selected}
            onChange={event => this.handleChange(event.target.value)}
            input={<Input id="name" />}
          >
            <MenuItem value="hai">Hai</MenuItem>
            <MenuItem value="olivier">Olivier</MenuItem>
            <MenuItem value="kevin">Kevin</MenuItem>
          </Select>
          {hasError && <FormHelperText>This is required!</FormHelperText>}
        </FormControl>
        <button type="button" onClick={() => this.handleClick()}>
          Submit
        </button>
      </form>
    );
  }
}

CodeSandBox 上的工作演示

Material UI 有其他类型的 Select(native) 也可以使用纯 HTML required 属性来标记元素为必需的。

<FormControl className={classes.formControl} required>
  <InputLabel htmlFor="name">Name</InputLabel>
  <Select
    native
    required
    value={this.state.name}
    onChange={this.handleChange}
    inputProps={{
      name: 'name',
      id: 'name'
    }}
  >
    <option value="" />
    <option value={"lala"}>lala</option>
    <option value={"lolo"}>lolo</option>
  </Select>
</FormControl>

PS https://material-ui.com/demos/selects/#native-select