You need to create new Angular FormControl and listen to its valueChange method. Here is an example:

HTML:

<div class="md-form">
  <mdb-select-2 placeholder="Choose your option" label="Example label">
    <mdb-select-filter
      [formControl]="searchInput">
    </mdb-select-filter>
    <mdb-select-option *ngFor="let option of filteredOptions | async" [value]="option">{{ option.label }}</mdb-select-option>
  </mdb-select-2>
</div>

TS:

  searchInput = new FormControl('');
  filteredOptions: Observable<any[]>;
  options = [
    { value: '1', label: 'Option 1' },
    { value: '2', label: 'Option 2' },
    { value: '3', label: 'Option 3' },
  ];

  ngOnInit() {
    this.filteredOptions = this.searchInput.valueChanges.pipe(
      startWith(''),
      map((value: string) => this.filter(value))
    );
  }

  filter(value: string): any[] {
    const filterValue = value.toLowerCase();
    return this.options.filter((option: any) => option.label.toLowerCase().includes(filterValue));
  }